# Lesson 10

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.

### 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 $$5x -15 - 20x+10$$.

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:

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

### 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

(From Unit 4, Lesson 4.)

### 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. $$9 - 7x < 6$$