How to Use Distributive Property to Solve an Equation

Step-by-Step Guide

1. 1

   Step 1: Multiply the term outside of the parentheses by each term in the parentheses.

   To do this, you are essentially distributing the outer term into the inner terms.
   
   Multiply the term outside the parentheses by the first term in the parentheses.
   
   Then multiply it by the second term.
   
   If there are more than two terms, keep distributing the term until there are no terms left.
   
   Keep whatever operation (plus or minus) is in the parentheses.2(x−3)=10{\displaystyle 2(x-3)=10} 2(x)−(2)(3)=10{\displaystyle 2(x)-(2)(3)=10} 2x−6=10{\displaystyle 2x-6=10}
2. 2

   Step 2: Combine like terms.

   Before you can solve the equation, you will have to combine like terms.
   
   Combine all numerical terms with each other.
   
   Separately, combine any variable terms.
   
   To simplify the equation, arrange the terms so the variables are on one side of the equals sign and the constants (numbers only) are on the other.2x−6=10{\displaystyle 2x-6=10}…..(original problem) 2x−6(+6)=10(+6){\displaystyle 2x-6(+6)=10(+6)}….. (Add 6 to both sides) 2x=16{\displaystyle 2x=16}….. (Variable on left; constant on right) , Solve for x{\displaystyle x} by dividing both sides of the equation by the coefficient in front of the variable.2x=16{\displaystyle 2x=16}…..(original problem) 2x/2=16/2{\displaystyle 2x/2=16/2}…..(divide both sides by 2) x=8{\displaystyle x=8}…..(solution)
3. 3

   Step 3: Solve the equation.

Detailed Guide

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