If I multiply a number by 2 and add 5 the result is always greater than the original number.
Determine, giving a reason, whether the above statement is always true, sometimes true or never true, and state, in exact form, the set of values of the number for which the statement is true.
257 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 7.1 Algebraic Fractions, 7.2 Dividing Polynomials, 7.3 The Factor Theorem, 7.4 Mathematical Proof, and 7.5 Methods of Proof. Each one has a worked solution and a mark scheme showing where the marks go.