Lesson 10

Different Options for Solving One Equation

Let’s think about which way is easier when we solve equations with parentheses.

Problem 1

Andre wants to buy a backpack. The normal price of the backpack is $40. He notices that a store that sells the backpack is having a 30% off sale. What is the sale price of the backpack?

(From Unit 4, Lesson 11.)

Problem 2

On the first math exam, 16 students received an A grade.  On the second math exam, 12 students received an A grade. What percentage decrease is that?

(From Unit 4, Lesson 12.)

Problem 3

Solve each equation.

  1. \(2(x-3) = 14\)
  2. \(\text-5(x-1) = 40\)
  3. \(12(x+10)=24\)
  4. \(\frac16(x+6)=11\)
  5. \(\frac57(x-9)=25\)

Problem 4

Select all expressions that represent a correct solution to the equation \(6(x+4)=20\).


\((20-4)\div 6\)










\((20-24)\div 6\)

Problem 5

Lin and Noah are solving the equation \(7(x+2)=91\).

Lin starts by using the distributive property. Noah starts by dividing each side by 7.

  1. Show what Lin's and Noah's full solution methods might look like.

  2. What is the same and what is different about their methods?