Rearranging Algebraic Equations to 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 = 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:

   7x = 14

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

   

2. 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 –[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: