Lesson 21

Combining Like Terms (Part 2)

Problem 1

  • Noah says that \(9x - 2x + 4x\) is equivalent to \(3x\), because the subtraction sign tells us to subtract everything that comes after \(9x\).
  • Elena says that \(9x - 2x + 4x\) is equivalent to \(11x\), because the subtraction only applies to \(2x\).

Do you agree with either of them? Explain your reasoning.

Solution

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Problem 2

Identify the error in generating an expression equivalent to \(4+2x-\frac12(10-4x)\). Then correct the error.

\(4+2x + \frac {\text{-}1}{2}(10 + \text-4x) \\ 4+2x +\text-5 +2x \\ 4+2x-5+2x \\ \text-1\)

Solution

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Problem 3

Select all expressions that are equivalent to \(5x -15 - 20x+10\).

A:

\(5x - (15+20x) + 10\)

B:

\(5x+\text-15+\text-20x+10\)

C:

\(5(x-3-4x+2)\)

D:

\(\text-5(\text-x +3+4x+\text-2)\)

E:

\(\text-15x-5\)

F:

\(\text-5(3x+1)\)

G:

\(\text-15(x - \frac13)\)

Solution

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Problem 4

The school marching band has a budget of up to $750 to cover 15 new uniforms and competition fees that total $300. How much can they spend for one uniform?

  1. Write an inequality to represent this situation.
  2. Solve the inequality and describe what it means in the situation.

Solution

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(From Unit 6, Lesson 14.)

Problem 5

Solve the inequality that represents each story. Then interpret what the solution means in the story.

  1. For every $9 that Elena earns, she gives \(x\) dollars to charity. This happens 7 times this month. Elena wants to be sure she keeps at least $42 from this month’s earnings. \(7(9-x) \geq 42\)
  2. Lin buys a candle that is 9 inches tall and burns down \(x\) inches per minute. She wants to let the candle burn for 7 minutes until it is less than 6 inches tall. \(9 - 7x < 6\)

Solution

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(From Unit 6, Lesson 16.)

Problem 6

A certain shade of blue paint is made by mixing \(1\frac12\) quarts of blue paint with 5 quarts of white paint. If you need a total of 16.25 gallons of this shade of blue paint, how much of each color should you mix?

Solution

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(From Unit 4, Lesson 3.)