Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Algebra - Basic equations.
Test Yourself 1 - Solutions.


 

There are several ways to solve each of the equations in this Exercise.
What you need to develop is a strategy which enables you to use a systematic approach
which will result in the fewest errors (so none!!).
A common approach is used in the solutions below.
Get used to that and then adapt it as you get good (and faster).
The more ways you understand and are good at - the better.

One line - 2 terms. 1. 2x = 6

Divide both sides by 2:

x = 6 ÷ 2 = 3		 2. 8x = 40

Divide bith sides by 8:

x = 40 ÷ 8 = 5
  3. 2x = 9

Divide both sides by 2:

x = 9 ÷ 2 = 4.5		 4. 4x = 14

Divide both sides by 4:

x = 14 ÷ 4 = 3.5
  5. 3x - 21 = 0

Divide both sides by 3 and add 21 to both sides:

3x = 21
Divide by 3: x = 21 ÷ 3 = 7		 6. 45 = 5x

Divide both sides by 5:

45 ÷ 5 = 9 = x
then reverse sides - so x = 9
One line - more than
2 terms.		 7. x - 9 = 21
Add 9 to both sides.
x = 30		 8. 5x - 4 = 16
Add 4 to both sides: 5x = 20
Then divide both sides by 5:
x = 4
  9. 3 + 4x = 15
Subrtact 3 from both sides: 4x = 12
Then divide both sides by 4:
x = 3		 10. 2 - 3x = -4
Subtract 2 from both sides: -3x = -6
Then divide both sides by -3:
x = 2
  11. 2x - 1 = 19
Add 1 to both sides: 2x = 20
Then divide both sides by 2:
x = 10		 12. 7 + 3x = x + 13
Subtract 7 from both sides and then subtract x from both sides:

2x = 6
Then divide both sides by 2:
x = 3
  13. 8 - 3x = x + 2 - 5x
Combine the x terms on the RHS: 8 - 3x = 2 - 4x
Then add 4x to both sides
8 + x = 2:
Subtract 8 from both sides:
x = -6		 14. 2 - x = 5x + 8
Add x to both sides: 2 = 6x + 8
Then subtract 8 from both sides:
6x = -6
then divide both sides by 6
x = -1
  15. x + 9 = 11x - 21
Subtract x from both sides:
9 = 10x - 21
Then add 21 to both sides:
30 = 10x
Divide both sides by 10
x = 3 		16. 8x - 13 = 2x - 13
Subtract 2x from both sides:
6x - 13 = -13
Then add 13 to both sides:
6x = 0
Divide both sides by 6
x = 0
One line - brackets. 17. 4( x - 7) = 2x + 10
Expand the brackets:
4x - 28 = 2x + 10
Subtract 2x from both sides:
2x - 28 = 10
Then add 28 to both sides:
2x = 38
Divide both sides by 2
x = 19		 18. 5x = 2 + 3(2x - 2)
Expand the brackets:
5x = 2 + 6x - 6
Subtract 6x from both sides and add the numbers:
-x = -4
x = 4
  19. 3(3x - 4) -2(1 - 2x) = -53

Expand both brackets:
9x - 12 - 2 +4x = -53
Bring like terms on LHS together:
13x - 14 = -53
Then add 14 to both sides:
13x = -39
Divide both sides by 13
x = -3		 20. 2(1 - 3x) + 4x = 2(x + 1)

Expand the brackets:
2 - 6x = 2x + 2
Add 6x to both sides:
2 = 8x + 2
Then subtract 2 from both sides:
8x =
Divide both sides by 8
x = 0
  21. 6x - 4 = 2(4x - 1)

Expand the brackets:
6x - 4 = 8x - 2
Subtract 6x from both sides:
-4 = 2x - 2
Then add 2 to both sides:
-2 = 2x
Divide both sides by 2
x = -1		 22. 5x - 2(x + 1) = 4(x - 6)

Expand the brackets:
5x - 2x - 2 = 4x - 24
Combine like terms on both sides:
3x - 2 = 4x - 24
Then subtract 3x from both sides:
-2 = x - 24
Add 24 to both sides
x = 22
Fractions - two terms. 23. 24.
  25. 26.
Fractions with more than
2 terms.		 27. 28.
  29. 30.
  31. 32.
  33. 34.
  35. 36.
  37. 38.
  39. 40.