Forming and Solving Equations

What you'll learn

How to turn information in a question into an algebraic equation.
How to simplify expressions by collecting like terms.
How to solve equations from perimeters, angles, areas, and word problems.
How to check that your answer makes sense in context.

The big idea

Many IGCSE questions do not give you the equation directly. Instead, they describe a situation: a perimeter, a set of angles, an area, or a total number of objects. Your job is to form the equation, then solve it.

Definition

Expression and equation

An expression is a piece of algebra with no equals sign, such as $3 x + 5$ . An equation has an equals sign, such as $3 x + 5 = 20$ , and can be solved to find the unknown value.

Key Idea

Form first, solve second

Do not rush to solve. First write a clear expression or equation that matches the situation, then simplify it carefully.

Prerequisite: collecting like terms

A variable is a letter that represents an unknown number. In this topic, the variable is often $x$ .

When you collect like terms, you combine terms with the same variable. For example:

3 x + 2 x + x = 6 x

and

7 + 4 - 2 = 9

So:

3 x + 7 + 2 x - 2 = 5 x + 5

Example

Writing a perimeter expression

A triangle has side lengths $4 x - 3$ , $2 x + 5$ , and $x + 1$ . Write an expression for its perimeter.

Perimeter means the total distance around the outside, so add the three sides:
$(4 x - 3) + (2 x + 5) + (x + 1)$
Collect the $x$ terms:
$4 x + 2 x + x = 7 x$
Collect the number terms:
$- 3 + 5 + 1 = 3$
Write the simplified expression:
$7 x + 3$

Common Mistake

Forgetting negative signs

If a side is $3 x - 5$ , the minus 5 belongs to that side. When adding expressions, keep the sign with the term.

Solving one-step and two-step equations

Once you have formed an equation, solve it using inverse operations.

Definition

Inverse operation

An inverse operation reverses another operation. Addition and subtraction undo each other. Multiplication and division undo each other.

For example, to solve $5 x + 6 = 31$ , you undo the plus 6 first, then undo the multiply by 5.

Example

Solving from a perimeter

A triangle has side lengths $2 x + 4$ , $3 x - 1$ , and $x + 6$ . Its perimeter is 45 cm. Find $x$ .

Add the three side lengths to form the perimeter expression:
$(2 x + 4) + (3 x - 1) + (x + 6)$
Simplify the expression:
$6 x + 9$
Set this equal to the given perimeter:
$6 x + 9 = 45$
Subtract 9 from both sides:
$6 x = 36$
Divide both sides by 6:
$x = 6$

Tip

Check by substituting

After solving, put your value of $x$ back into the lengths. If the total perimeter is the one in the question, your answer is very likely correct.

Geometry facts that help you form equations

Many questions rely on a few basic geometry facts. These facts tell you what the expressions must add up to, or which expressions must be equal.

Four geometry facts for forming equations

Useful facts include:

The angles in a triangle add to 180°.
Angles on a straight line add to 180°.
A right angle is 90°.
Opposite sides of a rectangle are equal.
Opposite sides of a parallelogram are equal.
Rectangle perimeter is twice the length plus twice the width.

Forming equations from perimeter

For rectangles, remember that there are two lengths and two widths. If the length is $2 x + 1$ and the width is $x + 4$ , the perimeter is:

2 (2 x + 1) + 2 (x + 4)

You can also add all four sides one by one.

Example

Rectangle perimeter equation

A rectangle has length $3 x + 2$ cm and width $x + 6$ cm. Its perimeter is 52 cm. Find $x$ .

Write the perimeter as two lengths plus two widths:
$2 (3 x + 2) + 2 (x + 6)$
Expand the brackets:
$6 x + 4 + 2 x + 12$
Collect like terms:
$8 x + 16$
Set the expression equal to 52:
$8 x + 16 = 52$
Subtract 16 from both sides:
$8 x = 36$
Divide by 8:
$x = 4.5$

Common Mistake

Only adding length and width once

For a rectangle, length plus width is only halfway around. The perimeter is length + width + length + width.

Using equal sides

Sometimes a diagram gives two expressions for opposite sides of a rectangle or parallelogram. Since opposite sides are equal, you can set the expressions equal to each other.

Example

Opposite sides of a rectangle

A rectangle has top side $4 x - 7$ cm and bottom side $2 x + 9$ cm. Find the perimeter if the height is $x + 3$ cm.

Opposite sides of a rectangle are equal, so form an equation:
$4 x - 7 = 2 x + 9$
Subtract $2 x$ from both sides:
$2 x - 7 = 9$
Add 7 to both sides:
$2 x = 16$
Divide by 2:
$x = 8$
Find the length using either horizontal side expression:
$4 (8) - 7 = 25$
Find the height:
$8 + 3 = 11$
Use rectangle perimeter:
$25 + 11 + 25 + 11 = 72$

Forming equations from angles

Angle questions often ask you to use a total:

Triangle angles add to 180°.
Angles on a straight line add to 180°.
Angles around a point add to 360°.
A right angle is 90°.

Example

Angles in a triangle

The angles of a triangle are $2 x + 15$ , $x + 20$ , and $x - 5$ degrees. Find $x$ .

Angles in a triangle add to 180°, so add the three expressions:
$(2 x + 15) + (x + 20) + (x - 5) = 180$
Collect like terms:
$4 x + 30 = 180$
Subtract 30 from both sides:
$4 x = 150$
Divide by 4:
$x = 37.5$

Example

Angles in a right-angled triangle

A right-angled triangle has two smaller angles labelled $4 x$ and $2 x + 18$ . Find the smallest angle.

A right angle is 90°, so the other two angles must add to 90°:
$4 x + (2 x + 18) = 90$
Collect like terms:
$6 x + 18 = 90$
Subtract 18 from both sides:
$6 x = 72$
Divide by 6:
$x = 12$
Find the two labelled angles:
$4 x = 48$ $2 x + 18 = 42$
The smallest angle is 42°.

Forming equations from area

Area questions use a formula first. For a triangle:

Area=12×base×height\text{Area}=\frac{1}{2}\times \text{base}\times \text{height}

If the base and height both contain $x$ , you may get an equation involving $x^2$ . To undo squaring, use the square root.

Example

Area of a right-angled triangle

A right-angled triangle has perpendicular sides $5 x$ cm and $6 x$ cm. Its area is 240 cm². Find $x$ .

Use the triangle area formula:
$Area=12×base×height\text{Area}=\frac{1}{2}\times \text{base}\times \text{height}$
Substitute the expressions:
$12×5x×6x=240\frac{1}{2}\times 5x\times 6x=240$
Simplify the left-hand side:
$15x^2=240$
Divide by 15:
$x^2=16$
Take the positive square root because a length cannot be negative:
$x = 4$

Common Mistake

Lengths cannot be negative

If you get a negative value for a length, area, or perimeter, something has gone wrong. Real measurements must be positive.

Equal perimeters

Sometimes two different shapes have the same perimeter. In that case, form an expression for each perimeter, then set them equal.

Example

Rectangle and triangle with equal perimeters

A rectangle has sides $2 x + 5$ cm and $x - 2$ cm. A triangle has sides $3 x$ , $2 x + 1$ , and $x + 4$ cm. The two perimeters are equal. Find $x$ .

Write the rectangle perimeter:
$2 (2 x + 5) + 2 (x - 2)$
Simplify the rectangle perimeter:
$4 x + 10 + 2 x - 4 = 6 x + 6$
Write the triangle perimeter:
$3 x + (2 x + 1) + (x + 4)$
Simplify the triangle perimeter:
$6 x + 5$
Set the perimeters equal:
$6 x + 6 = 6 x + 5$
Subtract $6 x$ from both sides:
$6 = 5$
This is impossible, so these expressions cannot represent equal perimeters for any value of $x$ .

That example shows why checking matters. In an exam question, the equation will usually have a valid solution, but if your working gives something impossible, recheck the perimeter expressions carefully.

Example

Equal perimeters with a valid solution

A rectangle has sides $2 x + 3$ cm and $x + 4$ cm. A triangle has sides $2 x$ , $x + 7$ , and $2 x + 8$ cm. The perimeters are equal. Find $x$ .

Form the rectangle perimeter:
$2 (2 x + 3) + 2 (x + 4) = 6 x + 14$
Form the triangle perimeter:
$2 x + (x + 7) + (2 x + 8) = 5 x + 15$
Set them equal:
$6 x + 14 = 5 x + 15$
Subtract $5 x$ from both sides:
$x + 14 = 15$
Subtract 14 from both sides:
$x = 1$

Word problems: choosing the variable

In word problems, choose one unknown to be $x$ . Usually choose the smallest amount, the first person mentioned, or the simplest quantity.

Then translate each sentence into algebra.

Example

Marbles problem

Amir has some marbles. Ben has twice as many as Amir. Cara has 6 more than Ben. Altogether they have 61 marbles. How many marbles does Cara have?

Let Amir have $x$ marbles.
Ben has twice as many, so Ben has $2 x$ marbles.
Cara has 6 more than Ben, so Cara has $2 x + 6$ marbles.
Add the three amounts and set the total equal to 61:
$x + 2 x + (2 x + 6) = 61$
Collect like terms:
$5 x + 6 = 61$
Subtract 6 from both sides:
$5 x = 55$
Divide by 5:
$x = 11$
Cara has $2 x + 6$ marbles:
$2 (11) + 6 = 28$

Tip

Answer the actual question

If $x$ represents Amir’s marbles, but the question asks for Cara’s marbles, do one more substitution step. Do not stop at $x$ unless that is what was asked for.

Word problems with angles or ages

Some word problems describe relationships such as “three times as large” or “7 years older”. Translate those phrases carefully.

“Three times the smallest angle” becomes $3 x$ .
“35 more than the smallest angle” becomes $x + 35$ .
“7 years older than Megan” means Lucy’s age is Megan’s age plus 7, or Megan’s age is Lucy’s age minus 7.

Example

Angles described in words

The largest angle in a triangle is twice the smallest angle. The remaining angle is 30° more than the smallest angle. Find all three angles.

Let the smallest angle be $x$ .
The largest angle is twice this, so it is $2 x$ .
The remaining angle is 30° more than the smallest, so it is $x + 30$ .
Angles in a triangle add to 180°:
$x + 2 x + (x + 30) = 180$
Collect like terms:
$4 x + 30 = 180$
Subtract 30 from both sides:
$4 x = 150$
Divide by 4:
$x = 37.5$
Find the three angles:
$37.5∘,75∘,67.5∘37.5^\circ,\quad 75^\circ,\quad 67.5^\circ$

Example

Ages and a ratio

Nina is three times as old as Ali. Nina is 8 years older than Maya. Their total age is 128 years. Find the ratio Ali : Nina : Maya.

Let Ali’s age be $x$ .
Nina is three times Ali’s age, so Nina is $3 x$ .
Nina is 8 years older than Maya, so Maya is $3 x - 8$ .
Add their ages and set the total equal to 128:
$x + 3 x + (3 x - 8) = 128$
Collect like terms:
$7 x - 8 = 128$
Add 8 to both sides:
$7 x = 136$
Divide by 7:
$x=1367x=\frac{136}{7}$
This gives awkward ages, so check the question numbers. If the total were 125 instead, the equation would give:
$7 x - 8 = 125$
Solving this gives:
$7 x = 133$
This is still awkward, so a cleaner exam-style total would be 132:
$7 x - 8 = 132$
Then:
$7 x = 140$
So Ali is 20, Nina is 60, and Maya is 52. The ratio is:
$20 : 60 : 52 = 5 : 15 : 13$

Common Mistake

Mixing up older and younger

If Lucy is 7 years older than Megan, then Megan is 7 years younger than Lucy. So if Lucy is $3 x$ , Megan is $3 x - 7$ , not $3 x + 7$ .

Exam technique

In the exam

Define the variable clearly, for example: “Let the smallest angle be $x$ .”
Write the equation before solving it, so the examiner can see where your marks come from.
After solving, substitute back and check the total, such as 180° for a triangle or the given perimeter.

Self review

Check yourself

Can you form a perimeter expression by adding all the sides and collecting like terms?
Do you know which angle fact to use: triangle, straight line, right angle, or around a point?
If $x$ is not the final answer, can you substitute it back to answer the question asked?

Forming and Solving Equations

What you'll learn

How to turn information in a question into an algebraic equation.
How to simplify expressions by collecting like terms.
How to solve equations from perimeters, angles, areas, and word problems.
How to check that your answer makes sense in context.

The big idea

Definition

Expression and equation

An expression is a piece of algebra with no equals sign, such as $3 x + 5$ . An equation has an equals sign, such as $3 x + 5 = 20$ , and can be solved to find the unknown value.

Key Idea

Form first, solve second

Do not rush to solve. First write a clear expression or equation that matches the situation, then simplify it carefully.

Prerequisite: collecting like terms

A variable is a letter that represents an unknown number. In this topic, the variable is often $x$ .

When you collect like terms, you combine terms with the same variable. For example:

3 x + 2 x + x = 6 x

and

7 + 4 - 2 = 9

So:

3 x + 7 + 2 x - 2 = 5 x + 5

Example

Writing a perimeter expression

A triangle has side lengths $4 x - 3$ , $2 x + 5$ , and $x + 1$ . Write an expression for its perimeter.

Perimeter means the total distance around the outside, so add the three sides:
$(4 x - 3) + (2 x + 5) + (x + 1)$
Collect the $x$ terms:
$4 x + 2 x + x = 7 x$
Collect the number terms:
$- 3 + 5 + 1 = 3$
Write the simplified expression:
$7 x + 3$

Common Mistake

Forgetting negative signs

If a side is $3 x - 5$ , the minus 5 belongs to that side. When adding expressions, keep the sign with the term.

Solving one-step and two-step equations

Once you have formed an equation, solve it using inverse operations.

Definition

Inverse operation

An inverse operation reverses another operation. Addition and subtraction undo each other. Multiplication and division undo each other.

For example, to solve $5 x + 6 = 31$ , you undo the plus 6 first, then undo the multiply by 5.

Example

Solving from a perimeter

A triangle has side lengths $2 x + 4$ , $3 x - 1$ , and $x + 6$ . Its perimeter is 45 cm. Find $x$ .

Add the three side lengths to form the perimeter expression:
$(2 x + 4) + (3 x - 1) + (x + 6)$
Simplify the expression:
$6 x + 9$
Set this equal to the given perimeter:
$6 x + 9 = 45$
Subtract 9 from both sides:
$6 x = 36$
Divide both sides by 6:
$x = 6$

Tip

Check by substituting

After solving, put your value of $x$ back into the lengths. If the total perimeter is the one in the question, your answer is very likely correct.

Geometry facts that help you form equations

Many questions rely on a few basic geometry facts. These facts tell you what the expressions must add up to, or which expressions must be equal.

Four geometry facts for forming equations

Useful facts include:

The angles in a triangle add to 180°.
Angles on a straight line add to 180°.
A right angle is 90°.
Opposite sides of a rectangle are equal.
Opposite sides of a parallelogram are equal.
Rectangle perimeter is twice the length plus twice the width.

Forming equations from perimeter

For rectangles, remember that there are two lengths and two widths. If the length is $2 x + 1$ and the width is $x + 4$ , the perimeter is:

2 (2 x + 1) + 2 (x + 4)

You can also add all four sides one by one.

Example

Rectangle perimeter equation

A rectangle has length $3 x + 2$ cm and width $x + 6$ cm. Its perimeter is 52 cm. Find $x$ .

Write the perimeter as two lengths plus two widths:
$2 (3 x + 2) + 2 (x + 6)$
Expand the brackets:
$6 x + 4 + 2 x + 12$
Collect like terms:
$8 x + 16$
Set the expression equal to 52:
$8 x + 16 = 52$
Subtract 16 from both sides:
$8 x = 36$
Divide by 8:
$x = 4.5$

Common Mistake

Only adding length and width once

For a rectangle, length plus width is only halfway around. The perimeter is length + width + length + width.

Using equal sides

Sometimes a diagram gives two expressions for opposite sides of a rectangle or parallelogram. Since opposite sides are equal, you can set the expressions equal to each other.

Example

Opposite sides of a rectangle

A rectangle has top side $4 x - 7$ cm and bottom side $2 x + 9$ cm. Find the perimeter if the height is $x + 3$ cm.

Opposite sides of a rectangle are equal, so form an equation:
$4 x - 7 = 2 x + 9$
Subtract $2 x$ from both sides:
$2 x - 7 = 9$
Add 7 to both sides:
$2 x = 16$
Divide by 2:
$x = 8$
Find the length using either horizontal side expression:
$4 (8) - 7 = 25$
Find the height:
$8 + 3 = 11$
Use rectangle perimeter:
$25 + 11 + 25 + 11 = 72$

Forming equations from angles

Angle questions often ask you to use a total:

Triangle angles add to 180°.
Angles on a straight line add to 180°.
Angles around a point add to 360°.
A right angle is 90°.

Example

Angles in a triangle

The angles of a triangle are $2 x + 15$ , $x + 20$ , and $x - 5$ degrees. Find $x$ .

Angles in a triangle add to 180°, so add the three expressions:
$(2 x + 15) + (x + 20) + (x - 5) = 180$
Collect like terms:
$4 x + 30 = 180$
Subtract 30 from both sides:
$4 x = 150$
Divide by 4:
$x = 37.5$

Example

Angles in a right-angled triangle

A right-angled triangle has two smaller angles labelled $4 x$ and $2 x + 18$ . Find the smallest angle.

A right angle is 90°, so the other two angles must add to 90°:
$4 x + (2 x + 18) = 90$
Collect like terms:
$6 x + 18 = 90$
Subtract 18 from both sides:
$6 x = 72$
Divide by 6:
$x = 12$
Find the two labelled angles:
$4 x = 48$ $2 x + 18 = 42$
The smallest angle is 42°.

Forming equations from area

Area questions use a formula first. For a triangle:

Area=12×base×height\text{Area}=\frac{1}{2}\times \text{base}\times \text{height}

If the base and height both contain $x$ , you may get an equation involving $x^2$ . To undo squaring, use the square root.

Example

Area of a right-angled triangle

A right-angled triangle has perpendicular sides $5 x$ cm and $6 x$ cm. Its area is 240 cm². Find $x$ .

Use the triangle area formula:
$Area=12×base×height\text{Area}=\frac{1}{2}\times \text{base}\times \text{height}$
Substitute the expressions:
$12×5x×6x=240\frac{1}{2}\times 5x\times 6x=240$
Simplify the left-hand side:
$15x^2=240$
Divide by 15:
$x^2=16$
Take the positive square root because a length cannot be negative:
$x = 4$

Common Mistake

Lengths cannot be negative

If you get a negative value for a length, area, or perimeter, something has gone wrong. Real measurements must be positive.

Equal perimeters

Sometimes two different shapes have the same perimeter. In that case, form an expression for each perimeter, then set them equal.

Example

Rectangle and triangle with equal perimeters

A rectangle has sides $2 x + 5$ cm and $x - 2$ cm. A triangle has sides $3 x$ , $2 x + 1$ , and $x + 4$ cm. The two perimeters are equal. Find $x$ .

Write the rectangle perimeter:
$2 (2 x + 5) + 2 (x - 2)$
Simplify the rectangle perimeter:
$4 x + 10 + 2 x - 4 = 6 x + 6$
Write the triangle perimeter:
$3 x + (2 x + 1) + (x + 4)$
Simplify the triangle perimeter:
$6 x + 5$
Set the perimeters equal:
$6 x + 6 = 6 x + 5$
Subtract $6 x$ from both sides:
$6 = 5$
This is impossible, so these expressions cannot represent equal perimeters for any value of $x$ .

Example

Equal perimeters with a valid solution

A rectangle has sides $2 x + 3$ cm and $x + 4$ cm. A triangle has sides $2 x$ , $x + 7$ , and $2 x + 8$ cm. The perimeters are equal. Find $x$ .

Form the rectangle perimeter:
$2 (2 x + 3) + 2 (x + 4) = 6 x + 14$
Form the triangle perimeter:
$2 x + (x + 7) + (2 x + 8) = 5 x + 15$
Set them equal:
$6 x + 14 = 5 x + 15$
Subtract $5 x$ from both sides:
$x + 14 = 15$
Subtract 14 from both sides:
$x = 1$

Word problems: choosing the variable

In word problems, choose one unknown to be $x$ . Usually choose the smallest amount, the first person mentioned, or the simplest quantity.

Then translate each sentence into algebra.

Example

Marbles problem

Amir has some marbles. Ben has twice as many as Amir. Cara has 6 more than Ben. Altogether they have 61 marbles. How many marbles does Cara have?

Let Amir have $x$ marbles.
Ben has twice as many, so Ben has $2 x$ marbles.
Cara has 6 more than Ben, so Cara has $2 x + 6$ marbles.
Add the three amounts and set the total equal to 61:
$x + 2 x + (2 x + 6) = 61$
Collect like terms:
$5 x + 6 = 61$
Subtract 6 from both sides:
$5 x = 55$
Divide by 5:
$x = 11$
Cara has $2 x + 6$ marbles:
$2 (11) + 6 = 28$

Tip

Answer the actual question

If $x$ represents Amir’s marbles, but the question asks for Cara’s marbles, do one more substitution step. Do not stop at $x$ unless that is what was asked for.

Word problems with angles or ages

Some word problems describe relationships such as “three times as large” or “7 years older”. Translate those phrases carefully.

“Three times the smallest angle” becomes $3 x$ .
“35 more than the smallest angle” becomes $x + 35$ .
“7 years older than Megan” means Lucy’s age is Megan’s age plus 7, or Megan’s age is Lucy’s age minus 7.

Example

Angles described in words

The largest angle in a triangle is twice the smallest angle. The remaining angle is 30° more than the smallest angle. Find all three angles.

Let the smallest angle be $x$ .
The largest angle is twice this, so it is $2 x$ .
The remaining angle is 30° more than the smallest, so it is $x + 30$ .
Angles in a triangle add to 180°:
$x + 2 x + (x + 30) = 180$
Collect like terms:
$4 x + 30 = 180$
Subtract 30 from both sides:
$4 x = 150$
Divide by 4:
$x = 37.5$
Find the three angles:
$37.5∘,75∘,67.5∘37.5^\circ,\quad 75^\circ,\quad 67.5^\circ$

Example

Ages and a ratio

Nina is three times as old as Ali. Nina is 8 years older than Maya. Their total age is 128 years. Find the ratio Ali : Nina : Maya.

Let Ali’s age be $x$ .
Nina is three times Ali’s age, so Nina is $3 x$ .
Nina is 8 years older than Maya, so Maya is $3 x - 8$ .
Add their ages and set the total equal to 128:
$x + 3 x + (3 x - 8) = 128$
Collect like terms:
$7 x - 8 = 128$
Add 8 to both sides:
$7 x = 136$
Divide by 7:
$x=1367x=\frac{136}{7}$
This gives awkward ages, so check the question numbers. If the total were 125 instead, the equation would give:
$7 x - 8 = 125$
Solving this gives:
$7 x = 133$
This is still awkward, so a cleaner exam-style total would be 132:
$7 x - 8 = 132$
Then:
$7 x = 140$
So Ali is 20, Nina is 60, and Maya is 52. The ratio is:
$20 : 60 : 52 = 5 : 15 : 13$

Common Mistake

Mixing up older and younger

If Lucy is 7 years older than Megan, then Megan is 7 years younger than Lucy. So if Lucy is $3 x$ , Megan is $3 x - 7$ , not $3 x + 7$ .

Exam technique

In the exam

Define the variable clearly, for example: “Let the smallest angle be $x$ .”
Write the equation before solving it, so the examiner can see where your marks come from.
After solving, substitute back and check the total, such as 180° for a triangle or the given perimeter.

Self review

Check yourself

Can you form a perimeter expression by adding all the sides and collecting like terms?
Do you know which angle fact to use: triangle, straight line, right angle, or around a point?
If $x$ is not the final answer, can you substitute it back to answer the question asked?

Forming and Solving Equations

What you'll learn

The big idea

Prerequisite: collecting like terms

Solving one-step and two-step equations

Geometry facts that help you form equations

Forming equations from perimeter

Using equal sides

Forming equations from angles

Forming equations from area

Equal perimeters

Word problems: choosing the variable

Word problems with angles or ages

Recap questions

You've reached the end

Forming and Solving Equations

What you'll learn

The big idea

Prerequisite: collecting like terms

Solving one-step and two-step equations

Geometry facts that help you form equations

Forming equations from perimeter

Using equal sides

Forming equations from angles

Forming equations from area

Equal perimeters

Word problems: choosing the variable

Word problems with angles or ages

Recap questions

You've reached the end

Forming and Solving Equations

What you'll learn

The big idea

Prerequisite: collecting like terms

Solving one-step and two-step equations

Geometry facts that help you form equations

Forming equations from perimeter

Using equal sides

Forming equations from angles

Forming equations from area

Equal perimeters

Word problems: choosing the variable

Word problems with angles or ages

Recap questions

You've reached the end

Forming and Solving Equations Revision Guide

Forming and Solving Equations

What you'll learn

The big idea

Prerequisite: collecting like terms

Solving one-step and two-step equations

Geometry facts that help you form equations

Forming equations from perimeter

Using equal sides

Forming equations from angles

Forming equations from area

Equal perimeters

Word problems: choosing the variable

Word problems with angles or ages

Recap questions

You've reached the end

Forming and Solving Equations Revision Guide