Remember to check your solution by substituting back into the original equation.
1. Solve the following equations. Show all of your working.
|
(a) |
x + 3 = 12 |
(f) |
6a = 42 |
|
(b) |
y + 5 = − 4 |
(g) |
- 3b = 12 |
|
(c) |
z − 5 = 15 |
(h) |
0 = 3 + p |
|
(d) |
- 2 = q − 4 |
(i)
|
|
|
(e) |
|
(j)
|
|
2. Solve the following equations:
|
(a) |
4y − 3 = 9 |
(f) |
5x + 8 = 14 |
|
(b) |
5x + 9 = 24 |
(g) |
3 − q = 5 |
|
(c) |
6x − 5 = 7 |
(h) |
- 2x − 6 = 4 |
|
(d) |
3 + 2x = 11 |
(i) |
4s + 6 = 3 |
|
(e) |
|
(j) |
|
3. Solve each of the following equations:
|
(a) |
|
(d) |
|
|
(b) |
|
(e) |
|
|
(c) |
|
(f) |
|
4. Expand the following brackets and then solve the equations:
|
(a) |
3(2a − 5) = 9 |
(d) |
6(d − 3) − d = 22 |
|
(b) |
4(b + 2) = 20 |
(e) |
- 2(e + 3) = 5 |
|
(c) |
8(7 − 3c) = 8 |
(f) |
5(2f − 6) = 2 |
5. Solve the following equations:
|
(a) |
|
(d) |
|
|
(b) |
|
(e) |
|
|
(c) |
|
(f) |
|
6. Solve the following equations:
|
(a) |
3a − 8 = 4a + 3 |
(d) |
4(d − 2) = 3(d + 6) |
|
(b) |
5b + 7 = b − 2 |
(e) |
e = 5(e − 2) + 3 |
|
(c) |
3 − c = 12 − 2c |
(f) |
8(x − 6) = 8x − 48 |
7. (a) I think of a number, multiply it by 5 and then take away 4 . The result is 31. What is the original number?
(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 even numbers whose sum is 78.
(d) Four times a number is 21 more than 55. What is the number?
(e) Suzanne is two years older than Adrienne. The total of their ages is 58 years. How old is each woman?
8. Solve the following inequations:
|
(a) |
x + 7 > 12 |
(e) |
3 − 4x > 11 |
|
(b) |
|
(f) |
- 2x < 6 |
|
(c) |
|
(g) |
|
|
(d) |
|
(h) |
3x + 7 < 2x − 6 |
