# 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 \(3x+5\).

\(\text-5+6x\)

\(5-6x\)

\(6x+5\)

\(6x-5\)

\(\text-6x+5\)

### Problem 3

Select **all** the statements that are true for any value of \(x\).

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

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

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

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

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

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

### Problem 4

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

- 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.
- Kiran read \(x\) books over the summer but was not invited to the party.

### 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?