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How to Isolate a Variable

Isolating a variable is a matter of separating and simplifying.


  • Step 1: Bring like terms together Bring like terms together. All equations have two sides. You want to perform the same operation on both sides of the equal sign. For the equation 4x –12 = -x + 8, 4x –12 is the left side and -x + 8 is the right side.
  • Step 2: Add variable to both sides Add the variable to both sides of the equation. For the equation 4x –12 = -x + 8, add x to both sides, changing it to 4x –12 + x = -x + 8 + x.
  • Step 3: Simplify Simplify the equation by adding the positive x and the negative x on the right side so they cancel each other out. The variable, x, is now on only one side of the equation: 5x – 12 = 8.
  • Step 4: Add the constant to both sides Add the "constant", the number not attached to x, on the side of the equation with the variable, to both sides of the equation.
  • Step 5: Simplify Simplify the equation. Combine like terms by adding eight and 12.
  • TIP: Put every term that contains the variable on one side of the equation and every term that does not contain a variable on the other side.
  • Step 6: Divide by the coefficient Divide both sides of the equation by the coefficient – the number attached to the variable.
  • Step 7: Solve Solve for x. The solution is x = 4.
  • Step 8: Test your solution Test your solution by plugging your answer into the original equation to be sure that it is correct.
  • FACT: Ancient Egyptians developed the math to solve linear equations as far back as 1850 BCE.

You Will Need

  • A pen or pencil
  • Paper

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