Pre-Algebra Practice Questions: Rearranging Equations to Isolate x

By Mark Zegarelli

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

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

Answers and explanations

  1. x = 2

    First, 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:

    PREALGEBRA_3201

    Second, combine like terms on both sides:

    7x = 14

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

    PREALGEBRA_3202

  2. x = –1

    Before 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
    –[2x + 14 + 1] = x – 12

    Next, remove the remaining parentheses, switching the sign of every term within that set:

    –2x – 14 – 1 = x – 12

    Now you can solve for x by, first, rearranging the terms of the equation:

    –2x – 14 – 1 + 12 = x
    –14 – 1 + 12 = x + 2x

    Then you combine like terms on both sides:

    –3 = 3x

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

    PREALGEBRA_3203