Solving equations when the term in x is negative

curriculum-key-fact
If the term in x is negative, tackle the equation in the same way - aim to get all xs on one side of the equation.

Example 1

Solve the equation:

5x - 2 = 12 - 2x

Your aim is to get all the unknown x terms on one side of the equation, so start by adding 2x to both sides:

7x - 2 = 12

Next add 2 to both sides:

7x = 14

And finally, divide by 7 to give:

x = 2

Again, you can check your answer in the original equation. So substitute x = 2 back into:

5x - 2 = 12 - 2x

(5 \times 2) - 2 = 12 - (2 \times 2)

10 - 2 = 12 - 4

8 = 8

This makes sense, so the value x = 2 is correct.

Example 2

Solve the equation:

4x = 10 - x

Add x to both sides to give:

5x = 10

To find x, divide both sides by 5:

x = 2

Question

Solve the equation:

3x + 1 = 16 - 2x

Start by adding 2x to both sides of the equation:

5x + 1 = 16

Then subtract {1} from each side:

5x = 15

Divide each side by 5 to give:

x = 3