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Chapter 9 · Questions · page 64 of 68

How do you solve an equation with parentheses?

Short answerDistribute to remove the parentheses, combine like terms, then solve. 2(x + 3) - 5 = 11 becomes 2x + 1 = 11, so x = 5.

levelAlgebra 1
standard8.EE.C.7b
practiceMulti-step equations

Parentheses hide terms. Distributing brings them out where you can combine them, and the long equation usually shrinks to a two-step one.

How to use it

  1. Distribute every number in front of parentheses, signs included.
  2. Combine like terms on each side.
  3. Collect the variable on one side and the numbers on the other.
  4. Divide, then check.

Example

2(x+3)−5=11⇒2x+1=11⇒2x=10⇒x=52(x + 3) - 5 = 11 \Rightarrow 2x + 1 = 11 \Rightarrow 2x = 10 \Rightarrow x = 5
−3(m−4)=21⇒−3m+12=21⇒−3m=9⇒m=−3-3(m - 4) = 21 \Rightarrow -3m + 12 = 21 \Rightarrow -3m = 9 \Rightarrow m = -3

Where it goes wrong

  • Distributing to the first term only.
  • Losing the sign when distributing a negative.

Related

Simplify each side firstThe distributive propertyA negative outside parentheses
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