OCR GCSE MATHS 8.1 LINEAR EQUATIONS(LATEST EDITION)

8.1 LINEAR EQUATIONS ©Cambridge University Press and OCR 2021 1 8 Equations 8.1 Linear equations • A linear equation is an equation where the highest power of the variable is 1, e.g. x + 2 = 5. • Variable means a letter representing an unknown number. • Solve means to find the unknown number represented by the letter. Exercise 1 1 Solve these equations without using a calculator. Write your answer as ‘x = …’. a b c d −2x = 12 e f g h WORKED EXAMPLES a Solve the equation 2(x − 5) = 8 to find the value of x. b Check your answer by substitution. Solution a Method 1 2(x − 5) = 8 Expand brackets. 2x − 10 = 8 Add 10 to both sides. 2x = 18 Divide both sides by 2. x = 9 Method 2 2(x − 5) = 8 Divide both sides by 2. x − 5 = 4 Add 5 to both sides. x = 9 b ‘Check your answer by substitution’ means replace each letter in the equation with your solution to see if the equation ‘balances’. 2(x − 5) = 8 Substituting x = 9 gives: 2(9 − 5) = 8 2 × 4 = 8 8 = 8 This balances, so we can be confident that our answer is correct. 8.1 LINEAR EQUATIONS ©Cambridge University Press and OCR 2021 2 2 Solve these equations. a 2a − 7 = 1 b 5b + 9 = 24 c 7c − 7 = 28 d 5d − 2 = 18 e 12e + 10 = 34 f 3f + 5 = −10 g −2g − 4 = 8 h −3h + 6 = −3 3 Solve these equations. a 3(x + 5) = 18 b 4(x − 3) = 12 c 7(x − 2) = 14 d 4(x − 3) = −16 e −2(x + 5) = 42 f −3(x − 4) = 9 g h 4 Solve these equations. a 3x + 2x = 15 b x + 2x − 3 = 12 c 4 − x + 2x = 8 d 3x − 4x = 5 + 3 e 2(x + 1) + 2x = 12 f 3 + 2(x + 5) = −9 g 2(x + 3) + 3(x + 1) = 6 h 3(x + 1) − 2(x + 3) = 4 WORKED EXAMPLE Solve the equation 6x − 5 = 3x + 1 to find the value of x. Solution 6x − 5 = 3x + 1 Subtract 3x from each side. 6x − 5 − 3x = 3x + 1 − 3x Add like terms. 3x − 5 = 1 Add 5 to each side. 3x = 6 Divide both sides by 3. x = 2 Check by substituting x = 2 back into the original equation. 6x − 5 = 3x + 1 6 × 2 − 5 = 3 × 2 + 1 7 = 7