## Equations and Inequations Exercise

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

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

 a. x + 2 = 13 f. 8a = 52 b. y + 5 = − 4 g. -2b = 12 c. z − 3 = 15 h. 0 = 2 + p d. -4 = q − 5 i. 4 = d⁄7 e. -4 = -e⁄5 j. c⁄4 = 1⁄2

2. Solve the following equations:

 a. 6y − 2 = 7 f. 4p + 11 = 23 b. 5y + 8 = 23 g. 2 − q = 5 c. 8x − 5 = 7 h. -2x − 8 = 5 d. 2 + 2s = 11 i. 5t + 8 = 3 e. p⁄2 + 3 = 4 j. 8 − x⁄3 = 12

3. Solve each of the following equations:

 a. 4x⁄5 = 20 d. -16 = 3p⁄2 b. 3y⁄4 = 5 e. 4⁄5 = p⁄2 c. -5z⁄8 = 15 f. 3z⁄5 = 1⁄4

4. Expand the following brackets and then solve the equations:

 a. 6(2a  5) = 6 d. 8(d − 2) − d = 26 b. 5(b + 2) =40 e. -2(e + 3) = 5 c. 6(7 − 2c) = -6 f. 5(2f − 8) = 2

5. Solve the following equations:

 a. d. b. e. c. f.

6. Solve the following equations:

 a. 2a − 7 = 5a + 2 d. 5(d − 2) = 2(d + 10) b. 5b + 7 = b − 2 e. e = 5(e − 2) + 2 c. 2 − c = 12 − 2c f. 8(f − 8) = 8f − 64

7.In each of the following questions form an equation and then solve it

(a) I think of a number, multiply it by 6 and then take away 9 . The result is 21. What is the original number?

(b) Juanita divides her age by 4 and adds 18. The result is the same as multiplying her age by two and subtracting 10.

How old is she?

(c) Find three consecutive numbers whose sum is 87.

(d) Four times a number plus 8 is 5 more than 55. What is the number?

(e) Sosefo is twenty two years older than Wiremu. The total of their ages is 80 years. How old is each man?

8. Solve the following inequations:

 a. x + 6 > 12 e. 4 − 5x > 19 b. 3x − 4 ≤ 5 f. -2x < 20 c. x⁄3 > 2 g. d. -3x⁄4 < 6 h. 4x + 7 < 2x − 8