## Linear Equations Exercise

Remember to check your solution by substituting back into the original equation.

1. Solve the following equations. Show all of your working.

 a. b. -2 = q − 4 c. d. 5x + 9 = 24 e. 3 − q = 5 f. 4x = 8x g, h. i. j. 3 + 2x = 11 k. -2x − 6 = 4 l. 5(2f − 6) = 2 m. 3(2a − 5) = 9 n. 4(b + 2) = 20 o. 8(7 − 3c) = 8 p. 6(d − 3) − d = 22 q. -2(e + 3) = 5 r.

2. Solve the following equation. Show all of your workings:

 a. 3a − 8 = 4a + 3 b. 4(d − 2) = 3(d + 6) c. 5b + 7 = b − 2 d. e = 5(e − 2) + 3 e.3 − c = 12 − 2c f. 8(x − 6) = 8x − 48 g. 8(x + 5) − 3(x − 2) = 3x -5 h. 6(x − 3) + 3x − 4(x − 1) = 0 i. 2(p − 6) = 4(2p + 3) + 2p

3. Solve the following equations. Show all of your working:

 a. b. c. d. e. f. g. h. i. j. k. l.

4. Write an equation to solve the following word problems:

(a) Bill divides his age by 7 and adds 17. The result is the same as dividing his age by 2 and adding 12. Find Bill's age.

(b) Richard divides his age by 7 and adds 16. The result is the same as multiplying his age by two and subtracting 10. How old is he?

(c) Find three consecutive odd numbers whose sum is 93.

(d) When the price of petrol was increased by 10 cents a litre, a motorist found that she could buy only 9 litres for the same money that she used to pay for 10 litres. Find the new price of petrol.

(e) Anna is two years older than David. The total of their ages is 22 years. How old is each person?