Solve Equations with Variables and Constants on Both Sides: example 2.33

Solve: $8 n - 4 = −2 n + 6 .$

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: $8 q - 5 = −4 q + 7 .$

How did it go?

Since $8 > −2$ , make the left side the “variable” side.
We don’t want variable terms on the right side—add $2 n$ to both sides to leave only constants on the right.
Combine like terms.
We don’t want any constants on the left side, so add $4$ to both sides.
Simplify.
The variable term is on the left and the constant term is on the right. To get the coefficient of $n$ to be one, divide both sides by 10.
Simplify.
Check:
Let $n = 1$ .

Since $8 > −2$ , make the left side the “variable” side.
We don’t want variable terms on the right side—add $2 n$ to both sides to leave only constants on the right.
Combine like terms.
We don’t want any constants on the left side, so add $4$ to both sides.
Simplify.
The variable term is on the left and the constant term is on the right. To get the coefficient of $n$ to be one, divide both sides by 10.
Simplify.
Check:
Let $n = 1$ .