# Solving equations and inequations

Remember when solving equations and to use the rule:

Change side, change operation

Look at the National 4 solving equations section before continuing.

### Example

Solve the equation $$- 2 - 3y = 11$$

$- 2 - 3y = 11$

$- 3y = 11 + 2$

Move the -2 over to the right hand side changes it to +2

-3 is multiplying on the left, so when moved to the right it divides

$- 3y = 13$

$y = \frac{{13}}{{ - 3}}\,or\,y = - 4\frac{1}{3}$

Now try the question below.

Question

Solve the equation $$35 = 5 - 6m$$ to find m.

$35 = 5 - 6m$

Move the -6m over to the left hand side, changing it to +6m.

$35 + 6m = 5$

Move the +35 to become -35

$6m = 5 - 35$

$6m = -30$

The 6 is multiplying on the left so now divide

$m = \frac{{ - 30}}{6} = \frac{{ - 5}}{1} = - 5$