Solving equations and inequations

Remember when solving equations and inequations to use the rule:

Change side, change operation

Look at the National 4 solving equations section before continuing.

Example

Solve the equation \(- 2 - 3y = 11\)

Answer

\[- 2 - 3y = 11\]

\[- 3y = 11 + 2\]

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

\[m = \frac{{ - 30}}{6} = \frac{{ - 5}}{1} = - 5\]