# Lesson 21

Combining Like Terms (Part 2)

Let’s see how to use properties correctly to write equivalent expressions.

### 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.

### Problem 2

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

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

### Problem 3

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

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

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

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

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

\(\text-15x-5\)

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

\(\text-15(x - \frac13)\)

### 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?

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

### Problem 5

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

- 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. \(7(9-x) \geq 42\)
- 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. \(9 - 7x < 6\)

### 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?