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# How to Isolate a Variable

Isolating a variable is a matter of separating and simplifying.

### Instructions

- 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