SOLVING EQUATIONS - ANSWERS

1.  ½x + 7 = 4

Multiply both sides by 2 (to get rid of the ½)
x + 14 = 8

Subtract 14 from both sides
x = -6
2.  2 - 6y = 1

Add 6y to both sides (to get rid of annoying minuses)
2 = 1 + 6y

Subtract 1 from both sides
1 = 6y

Divide both sides by 6
y = 1/6
3.  9 - 2x = 3 - 4x

Add 4x to both sides
9 + 2x = 3

Subtract 9 from both sides
2x = -6

Divide both sides by 2
x = -3
4.  2 - 7a = 3a Add 7a to both sides
2 = 10a

Divide both sides by 10
a = 2/10 = 1/5 (in its lowest terms)
5.  4(x + 3) = 16

Multiply the brackets on the left
4x + 12 = 16

Subtract 12 from both sides
4x = 4

Divide both sides by 4
x = 1
6. 5(x - 4) = 3x - 7

Multiply the brackets on the left
5x - 20 = 3x - 7

Add 20 to both sides
5x = 3x + 13

Subtract 3x from both sides
2x = 13

Divide both sides by 2
x = 13/2 (or x = 6 ½)

 
7. 4(3x - 2) - (7x + 8) = 2(x -5)

Multiply out the brackets
12x - 8 - 7x + 8 = 2x - 10

Gather like terms (notice that the -8 and 8 cancel)
12x - 7x = 2x - 10
i.e. 5x = 2x - 10

Subtract 2x from both sides
3x = -10

Divide both sides by 3
x = -10/3

8.