Solve Equations with Variables and Constants on Both Sides: example 8.32

Solve: $4 (x - 2) + 5 = −3 .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve: $2 (a - 4) + 3 = −1 .$

How did it go?


Simplify each side of the equation as much as possible. Distribute.
Combine like terms
The only $x$ is on the left side, so all variable terms are on one side of the equation.
Add 3 to both sides to get all constant terms on the other side of the equation.
Simplify.
Make the coefficient of the variable term equal to 1 by dividing both sides by 4.
Simplify.
Check: Let $x = 0$ .


Simplify each side of the equation as much as possible. Distribute.
Combine like terms
The only $x$ is on the left side, so all variable terms are on one side of the equation.
Add 3 to both sides to get all constant terms on the other side of the equation.
Simplify.
Make the coefficient of the variable term equal to 1 by dividing both sides by 4.
Simplify.
Check: Let $x = 0$ .