# Lesson 20

Combining Like Terms (Part 1)

Let's see how we can tell that expressions are equivalent.

### Problem 1

Andre says that $$10x+6$$ and $$5x+11$$ are equivalent because they both equal 16 when $$x$$ is 1. Do you agree with Andre? Explain your reasoning.

### Problem 2

Select all expressions that can be subtracted from $$9x$$ to result in the expression $$3x+5$$.

A:

$$\text-5+6x$$

B:

$$5-6x$$

C:

$$6x+5$$

D:

$$6x-5$$

E:

$$\text-6x+5$$

### Problem 3

Select all the statements that are true for any value of $$x$$.

A:

$$7x + (2x+7) = 9x+7$$

B:

$$7x + (2x - 1) = 9x + 1$$

C:

$$\frac12 x+(3 - \frac12 x)=3$$

D:

$$5x - (8 - 6x) =\text-x-8$$

E:

$$0.4x - (0.2x+8) =0.2x-8$$

F:

$$6x - (2x -4)=4x+4$$

### Problem 4

For each situation, would you describe it with $$x< 25$$, $$x > 25$$, $$x \leq 25$$, or $$x \geq 25$$?

1. The library is having a party for any student who read at least 25 books over the summer. Priya read $$x$$ books and was invited to the party.
2. Kiran read $$x$$ books over the summer but was not invited to the party.
3.
4.
(From Unit 6, Lesson 13.)

### Problem 5

Consider the problem: A water bucket is being filled with water from a water faucet at a constant rate. When will the bucket be full? What information would you need to be able to solve the problem?

(From Unit 2, Lesson 9.)