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forms."},{"text":"Both sides have the same numbers.","correct":false,"explanation":"The two sides do not need to contain identical numbers. The equals sign means both complete expressions have the same value."},{"text":"Both sides use the same operation.","correct":false,"explanation":"Different operations can appear on either side of an equation. The equals sign shows that the resulting values of both sides are the same."},{"text":"The right side gives the final answer.","correct":false,"explanation":"An equals sign does not simply introduce a final answer; it compares two expressions. Both sides must have the same value."}]},{"id":"a7056470-85c2-b39a-b261-f1189305a473","cardType":"cloze","points":null,"front":"A variable is a letter that stands for a [ ].","back":"A variable is a letter that stands for a number you do not know yet.","mcqOptions":[{"text":"number you do not know yet","correct":true,"explanation":"A variable uses a letter, such as $x$, to represent an unknown number that can be found by solving the equation."},{"text":"number that must equal zero","correct":false,"explanation":"A variable is not required to equal zero; zero is only one possible value. It represents a number whose value is not known yet."},{"text":"number printed after the equals sign","correct":false,"explanation":"A variable does not represent where a number is written in an equation. It stands for a number whose value is not known yet."},{"text":"number of operations in the equation","correct":false,"explanation":"A variable represents an unknown number, not a count of the equation’s operations. Operations are actions such as addition and multiplication."}]},{"id":"a2f68cfb-6b86-f153-1f81-8d3ae4dcb772","cardType":"cloze","points":null,"front":"An inverse operation [ ] another operation.","back":"An inverse operation undoes another operation.","mcqOptions":[{"text":"undoes","correct":true,"explanation":"An inverse operation reverses the effect of another operation. For example, subtraction undoes addition, while division undoes multiplication."},{"text":"repeats","correct":false,"explanation":"Repeating an operation applies it again rather than reversing it. An inverse operation undoes the original operation, such as subtracting after adding."},{"text":"replaces","correct":false,"explanation":"Replacing an operation does not necessarily reverse its effect. An inverse operation specifically undoes another operation to help isolate the variable."},{"text":"ignores","correct":false,"explanation":"Ignoring an operation leaves its effect unchanged. An inverse operation undoes that effect, such as dividing to undo multiplication."}]},{"id":"bfe5fc4c-d7fc-6832-c44c-fcd306f2f9bc","cardType":"basic","points":1,"front":"Find the missing number: $6+\\Box=17$.","back":"$$\\Box=11$","mcqOptions":[{"text":"$$\\Box=11$","correct":true,"explanation":"Subtracting $6$ from both sides gives the missing value: $17-6=11$. The check $6+11=17$ confirms the result."},{"text":"$$\\Box=23$","correct":false,"explanation":"Adding $6$ and $17$ produces $23$, but the missing number must be added to $6$. Subtracting gives $17-6=11$."},{"text":"$$\\Box=10$","correct":false,"explanation":"This is an off-by-one subtraction error. The required difference is $17-6=11$, and checking gives $6+11=17$."},{"text":"$$\\Box=12$","correct":false,"explanation":"This is an off-by-one calculation error because $6+12=18$, not $17$. The correct missing number is $17-6=11$."}]},{"id":"ff91b8d8-4a3b-52f3-3a88-7e89d5335908","cardType":"basic","points":1,"front":"Find the missing number: $19-\\Box=12$.","back":"$$\\Box=7$","mcqOptions":[{"text":"$$\\Box=7$","correct":true,"explanation":"The missing number is the difference between $19$ and $12$. Since $19-12=7$, substituting $7$ makes the equation true."},{"text":"$$\\Box=31$","correct":false,"explanation":"Adding $19$ and $12$ treats the equation as though the missing number were a total. Instead, $19-12=7$, so the missing number is $7$."},{"text":"$$\\Box=-7$","correct":false,"explanation":"The negative sign comes from reversing the subtraction incorrectly. Since $19-7=12$, the missing number is positive $7$."},{"text":"$$\\Box=8$","correct":false,"explanation":"This is an off-by-one subtraction error: $19-8=11$, not $12$. Calculating $19-12$ correctly gives the missing number $7$."}]},{"id":"f1307ae3-de1f-057e-d5fd-3a8d0671d6a8","cardType":"cloze","points":null,"front":"A one-step equation is solved using [ ].","back":"A one-step equation is solved using one inverse operation.","mcqOptions":[{"text":"one inverse operation","correct":true,"explanation":"Only one operation must be undone in a one-step equation, so applying its inverse once isolates the variable and solves the equation."},{"text":"two inverse operations","correct":false,"explanation":"Needing two inverse operations would normally indicate a two-step equation. A one-step equation requires exactly one inverse operation to isolate the variable."},{"text":"one identical operation","correct":false,"explanation":"Repeating the original operation does not undo it. A one-step equation is solved with one inverse operation, such as subtracting to undo addition."},{"text":"no inverse operations","correct":false,"explanation":"Without an inverse operation, the operation affecting the variable remains in place. A one-step equation requires one inverse operation to isolate the variable."}]},{"id":"23af32c5-4a5d-7546-b7e2-bebef163ac9a","cardType":"basic","points":1,"front":"In $x+7=19$, what inverse operation gets $x$ on its own?","back":"Subtract 7.","mcqOptions":[{"text":"Subtract 7.","correct":true,"explanation":"Subtracting $7$ undoes the addition of $7$. Applying it to both sides gives $x=19-7$, leaving $x$ on its own."},{"text":"Add 7.","correct":false,"explanation":"Adding another $7$ repeats the existing operation rather than undoing it. Subtracting $7$ from both sides isolates $x$."},{"text":"Subtract 19.","correct":false,"explanation":"The operation applied directly to $x$ is adding $7$, so its inverse is subtracting $7$, not subtracting the right-hand value."},{"text":"Divide by 7.","correct":false,"explanation":"Division by $7$ is the inverse of multiplication by $7$, not addition. Subtracting $7$ is required to undo $x+7$."}]},{"id":"899fd4e1-b206-7c1c-ff08-5681bdec9a89","cardType":"basic","points":1,"front":"Solve $x+7=19$.","back":"$$x=12$","mcqOptions":[{"text":"$$x=12$","correct":true,"explanation":"Subtracting $7$ from both sides gives $x=19-7=12$. Checking confirms that $12+7=19$."},{"text":"$$x=26$","correct":false,"explanation":"Adding $7$ to $19$ applies the wrong operation and gives $26$. Subtracting $7$ from both sides instead gives $x=12$."},{"text":"$$x=11$","correct":false,"explanation":"This is an off-by-one subtraction error because $11+7=18$, not $19$. Correctly calculating $19-7$ gives $x=12$."},{"text":"$$x=133$","correct":false,"explanation":"Multiplying $19$ by $7$ confuses addition with multiplication and does not undo $+7$. The inverse operation is subtraction, giving $x=12$."}]},{"id":"e213182f-4efe-9a17-b9c5-ab586769818f","cardType":"basic","points":1,"front":"In $m-6=10$, what inverse operation gets $m$ on its own?","back":"Add 6.","mcqOptions":[{"text":"Add 6.","correct":true,"explanation":"Adding 6 to both sides reverses the subtraction of 6. This leaves $m$ alone on the left and gives $m=16$."},{"text":"Subtract 6.","correct":false,"explanation":"Subtracting 6 again does not undo the original subtraction; it produces $m-12$. The inverse of subtracting 6 is adding 6 to both sides."},{"text":"Add 10.","correct":false,"explanation":"Using the number on the right as the operation does not cancel the $-6$. Add 6 to both sides because inverse operations undo each other."},{"text":"Divide by 6.","correct":false,"explanation":"Division would undo multiplication by 6, not subtraction of 6. Add 6 to both sides to cancel the $-6$ and isolate $m$."}]},{"id":"69e1d0d4-9d90-b494-f918-5b794145fad2","cardType":"basic","points":1,"front":"Solve $m-6=10$.","back":"$$m=16$","mcqOptions":[{"text":"$$m=16$","correct":true,"explanation":"Adding 6 to both sides gives $m=10+6=16$. Substituting 16 confirms the solution because $16-6=10$."},{"text":"$$m=4$","correct":false,"explanation":"Subtracting 6 from 10 applies the operation again instead of reversing it. Add 6 to both sides, giving $m=10+6=16$."},{"text":"$$m=-16$","correct":false,"explanation":"Introducing a negative sign is an unnecessary sign error. Adding 6 to both sides isolates the variable and gives the positive value $m=16$."},{"text":"$$m=60$","correct":false,"explanation":"Multiplying 10 by 6 confuses subtraction with multiplication. The inverse of subtracting 6 is adding 6, so $m=16$."}]},{"id":"f8bf0ed7-827a-2c5c-3544-cd0164b338e7","cardType":"cloze","points":null,"front":"The difference is the [ ] between two numbers.","back":"The difference is the gap between two numbers.","mcqOptions":[{"text":"gap","correct":true,"explanation":"A difference describes the gap between two numbers. It is found by subtracting one number from the other."},{"text":"sum","correct":false,"explanation":"A sum is the result of addition, not the separation between values. The difference is the gap between two numbers and is found using subtraction."},{"text":"product","correct":false,"explanation":"A product is the result of multiplication, so it does not describe how far apart two values are. The difference is their gap."},{"text":"quotient","correct":false,"explanation":"A quotient is the result of division, not subtraction. The difference means the gap between two numbers, found by subtracting them."}]},{"id":"33e7806c-7595-9955-1636-4bb2c1a9ad18","cardType":"basic","points":1,"front":"For $23-n=14$, what calculation finds the amount taken away?","back":"$$23-14=9$","mcqOptions":[{"text":"$$23-14=9$","correct":true,"explanation":"Subtracting the amount left from the starting amount finds what was taken away. Since $23-14=9$, the missing amount is 9."},{"text":"$$23+14=37$","correct":false,"explanation":"Adding combines the starting and remaining amounts rather than finding what was removed. Subtract the amount left from the start: $23-14=9$."},{"text":"$$14-23=-9$","correct":false,"explanation":"Reversing the subtraction creates a negative result even though the amount taken away is positive. Calculate starting amount minus remaining amount: $23-14=9$."},{"text":"$$23-9=14$","correct":false,"explanation":"This checks that removing 9 leaves 14, but it already assumes the missing amount is known. To find it directly, calculate $23-14=9$."}]},{"id":"5c545532-acbd-ce0f-f4b0-4fcc5c381157","cardType":"basic","points":1,"front":"Solve $23-n=14$.","back":"$$n=9$","mcqOptions":[{"text":"$$n=9$","correct":true,"explanation":"In $23-n=14$, $n$ is the difference between 23 and 14. Calculating $23-14$ gives $n=9$, and $23-9=14$ confirms it."},{"text":"$$n=37$","correct":false,"explanation":"Adding 23 and 14 does not find the amount subtracted from 23. The missing amount is the difference, so $n=23-14=9$."},{"text":"$$n=-9$","correct":false,"explanation":"Calculating $14-23$ reverses the required subtraction and creates an incorrect negative value. The amount taken away is $23-14=9$, so $n=9$."},{"text":"$$n=14$","correct":false,"explanation":"The 14 is the result after $n$ has been subtracted, not the value of $n$. The missing amount is $23-14=9$."}]},{"id":"3b6140a0-4f18-1e85-ecc1-c7d532a01153","cardType":"cloze","points":null,"front":"When a number is written next to a variable, such as $5p$, it means [ ].","back":"When a number is written next to a variable, such as $5p$, it means multiply.","mcqOptions":[{"text":"multiply","correct":true,"explanation":"Writing a number directly beside a variable indicates multiplication. Therefore, $5p$ means $5$ multiplied by $p$."},{"text":"divide","correct":false,"explanation":"Division is normally shown using a fraction bar or division symbol. A number written beside a variable means multiply, so $5p$ means $5\\times p$."},{"text":"add","correct":false,"explanation":"Addition requires a plus sign, as in $5+p$. Writing the terms together means multiplication, so $5p$ is $5$ multiplied by $p$."},{"text":"subtract","correct":false,"explanation":"Subtraction requires a minus sign, as in $5-p$. A number placed directly next to a variable indicates multiplication, so $5p$ means $5\\times p$."}]},{"id":"31529cf7-39d5-048e-d8ec-dc12e972d78a","cardType":"basic","points":1,"front":"Solve $7a=42$.","back":"$$a=6$","mcqOptions":[{"text":"$$a=6$","correct":true,"explanation":"Since $7a$ means $7\\times a$, divide both sides by 7. This gives $a=42\\div7=6$."},{"text":"$$a=35$","correct":false,"explanation":"Subtracting 7 from 42 does not undo multiplication by 7. Divide both sides by 7 instead, giving $a=42\\div7=6$."},{"text":"$$a=49$","correct":false,"explanation":"Adding 7 to 42 treats $7a$ as though it meant $a+7$. It means $7\\times a$, so division gives $a=6$."},{"text":"$$a=294$","correct":false,"explanation":"Multiplying 42 by 7 applies the same operation rather than its inverse. Divide 42 by 7 to isolate $a$, giving $a=6$."}]},{"id":"c6476a0c-8806-d7e6-b968-0c0ca1991a34","cardType":"basic","points":1,"front":"Rewrite $r+r+r$ using multiplication shorthand.","back":"$$3r$","mcqOptions":[{"text":"$$3r$","correct":true,"explanation":"There are three identical $r$ terms being added. Repeated addition is written as multiplication, so $r+r+r=3\\times r=3r$."},{"text":"$$r^3$","correct":false,"explanation":"A power of 3 represents multiplication, $r\\times r\\times r$, not repeated addition. Three added $r$ terms combine to make $3r$."},{"text":"$$2r$","correct":false,"explanation":"This counts only two of the three identical terms. Each $r$ contributes one to the coefficient, so $r+r+r=3r$."},{"text":"$$3+r$","correct":false,"explanation":"The 3 counts how many copies of $r$ are present, so it must be a coefficient rather than a separate term. The shorthand is $3r$."}]},{"id":"c07849fb-3f35-74a2-5a08-cb60b2322ce8","cardType":"basic","points":1,"front":"Solve $r+r+r=27$.","back":"$$r=9$","mcqOptions":[{"text":"$$r=9$","correct":true,"explanation":"There are three identical terms, so $3r=27$. Dividing both sides by $3$ gives $r=9$, and checking gives $9+9+9=27$."},{"text":"$$r=27$","correct":false,"explanation":"This treats the total as the value of each term. Since three lots of $r$ equal $27$, divide by $3$ to obtain $r=9$."},{"text":"$$r=8$","correct":false,"explanation":"This likely comes from an arithmetic or counting slip. Three lots of $8$ make $24$, not $27$; dividing $27$ by $3$ gives $r=9$."},{"text":"$$r=81$","correct":false,"explanation":"This multiplies $27$ by $3$ instead of dividing by the number of equal terms. Since $3r=27$, the correct value is $r=9$."}]},{"id":"b9dd0822-1cd5-8d50-15c9-55a3c792e808","cardType":"cloze","points":null,"front":"The fraction bar in a fraction means [ ].","back":"The fraction bar in a fraction means divide.","mcqOptions":[{"text":"divide","correct":true,"explanation":"A fraction represents the numerator divided by the denominator. For example, $\\frac{10}{2}$ means $10\\div2$, which equals $5$."},{"text":"multiply","correct":false,"explanation":"Multiplication is represented by symbols such as $\\times$, not by a fraction bar. The fraction bar means divide, with the numerator divided by the denominator."},{"text":"add","correct":false,"explanation":"A fraction bar does not combine the numerator and denominator by addition. It means divide, so $\\frac{a}{b}$ represents $a\\div b$."},{"text":"subtract","correct":false,"explanation":"Subtraction uses a minus sign rather than a fraction bar. The fraction bar means divide, with the quantity above divided by the quantity below."}]},{"id":"104e8fd8-100f-4474-a836-79e5be3f6e20","cardType":"basic","points":1,"front":"Solve $\\frac{d}{2}=7.5$.","back":"$$d=15$","mcqOptions":[{"text":"$$d=15$","correct":true,"explanation":"The equation says half of $d$ is $7.5$. Multiplying both sides by $2$ gives $d=15$, and $15\\div2=7.5$ confirms it."},{"text":"$$d=3.75$","correct":false,"explanation":"This divides $7.5$ by $2$ rather than using the inverse operation. To undo division by $2$, multiply by $2$, giving $d=15$."},{"text":"$$d=9.5$","correct":false,"explanation":"This adds $2$ to $7.5$, confusing the denominator with a term being subtracted. Undoing division by $2$ requires multiplication, so $d=15$."},{"text":"$$d=5.5$","correct":false,"explanation":"This subtracts $2$ from $7.5$, but the equation divides $d$ by $2$. Multiplying both sides by $2$ correctly gives $d=15$."}]},{"id":"798ab3d6-dfe1-f39b-53a7-7103f249a896","cardType":"basic","points":1,"front":"Solve $\\frac{30}{y}=6$.","back":"$$y=5$","mcqOptions":[{"text":"$$y=5$","correct":true,"explanation":"Multiplying both sides by $y$ gives $30=6y$. Dividing by $6$ then gives $y=5$, and $30\\div5=6$ confirms the answer."},{"text":"$$y=180$","correct":false,"explanation":"This multiplies $30$ by $6$, overlooking that $y$ is the divisor. From $30=6y$, divide $30$ by $6$ to get $y=5$."},{"text":"$$y=0.2$","correct":false,"explanation":"This reverses the required division and calculates $6\\div30$. The equation asks what divides $30$ to make $6$, so $y=30\\div6=5$."},{"text":"$$y=24$","correct":false,"explanation":"This subtracts $6$ from $30$, treating the equation like $30-y=6$. Here $y$ is a divisor, and solving $30=6y$ gives $y=5$."}]},{"id":"cdbe0521-de94-26a2-e68d-7137cbce1513","cardType":"basic","points":1,"front":"How do you check an answer to an equation?","back":"Substitute it into the original equation.","mcqOptions":[{"text":"Substitute it into the original equation.","correct":true,"explanation":"Replacing the unknown with the proposed answer checks whether both sides of the original equation have the same value. If they do, the answer satisfies the equation."},{"text":"Subtract it from the original equation.","correct":false,"explanation":"Subtracting the answer from an equation does not directly test whether it satisfies the original relationship. Substitute the answer for the unknown and compare both sides instead."},{"text":"Multiply it by the original equation.","correct":false,"explanation":"Multiplying by the answer changes the equation rather than checking the proposed solution. The reliable check is to substitute the answer into the original equation."},{"text":"Round it before using the original equation.","correct":false,"explanation":"Rounding can alter an exact solution and make a valid answer appear wrong. Substitute the unrounded answer into the original equation and verify that both sides match."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Component 1"},"heading":"Solving One Step Equations","title":"Solving One Step Equations Flashcards","topbar":{"backHref":"/gcse/maths/eduqas/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"e9a555a4-6440-4aba-b5c5-0dce17086fe4","walled":"$L39"}],"$L3a","$L3b"]