GRE equation solving refresher

Posted on September 25, 2009 by GRE Tutor

Equation Solving

Isolate the variable by performing the same operation to both sides of the equation

Tip: What you do to one side of the equation, you must do to the other side.

Examples:

• x + 7 = 11
  subtract 7 from both sides and you get
  x = 4
• x – 3 = 12
  add 3 to both sides and you get
  x = 15
• 5x = 30
  divide both sides by 5 and you get
  x = 6
• 3x + 7 = 19
  subtract 7 from both sides and you get
  3x = 12
  divide both sides by 3 and you get
  x = 4
• 2x + 6 = 7x – 24
  subtract 2x from both sides and you get
  6 = 5x – 24
  add 24 to both sides and you get
  30 = 5x
  divide both sides by 5 and you get
  x = 6
• 3(2x-1) + 4x – 11 = 8
  expand the equation and you get
  6x – 3 + 4x – 11 = 8
  simplify the equation and you get
  10x – 14 = 8
  add 14 to both sides and you get
  10x = 22
  divide both sides by 10 and you get
  x = 2.2

Tip: To check your answers, plug in the value for x into the equation.

Practice questions to solve each equation for x:

1. 2x – 3 = 15
2. 2/3 x = 14
3. 5x + 8 = 23
4. 10 – 2x = 14
5. 3x + 2x + x = 66
6. 2(5x -8) = 44
7. 4x + 7 – 2 – 6x = 17
8. 7x – 8 = 3x + 12
9. -3(x – 1) = -21
10. 2(2x + 3) = 3x – 11
11. -2x + 13 = 22
12. x + x + 3 + x + 5 = 4x – 1
13. -3(2 – 3x) = 3(x + 2) – 4x
14. -19 = 5 – 8x
15. 2x + 2 + 7x – 9 = x – 2 + 3x + 10