# Pre-Algebra Practice Questions: Rearranging Equations to Isolate x

A quick method for solving algebra problems is to re-arrange the equation by placing all *x* terms on one side of the equal sign and all constants (non-*x* terms) on the other side. Essentially, you’re doing the addition and subtraction without showing it. You can then isolate *x*.

## Practice questions

- Rearrange the equation 10
*x*+ 5 = 3*x*+ 19 to solve for*x*. - Solve –[2(
*x*+ 7) + 1] =*x*– 12 for*x*.

## Answers and explanations

*x*= 2First, rearrange the terms of the equation so that the

*x*terms are on one side and the constants are on the other. In this case, you can do this in two steps:Second, combine like terms on both sides:

7

*x*= 14The third and final step is to divide (in this case, by 7) to isolate

*x*:*x*= –1Before you can begin rearranging terms, remove the parentheses on the left side of the equation. Start with the inner parentheses, multiplying 2 by every term inside that set:

–[2(

*x*+ 7) + 1] =*x*– 12

–[2*x*+ 14 + 1] =*x*– 12Next, remove the remaining parentheses, switching the sign of every term within that set:

–2

*x*– 14 – 1 =*x*– 12Now you can solve for

*x*by, first, rearranging the terms of the equation:–2

*x*– 14 – 1 + 12 =*x*

–14 – 1 + 12 =*x*+ 2*x*Then you combine like terms on both sides:

–3 = 3

*x*Finally, you divide (in this example, by 3) to isolate

*x*: