# Lesson 9

Combining Like Terms (Part 1)

### 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.

### Solution

(From Unit 4, Lesson 3.)

### Problem 5

A line is represented by the equation $$\frac{y}{x-2}=\frac{3}{11}$$. What are the coordinates of some points that lie on the line? Graph the line on graph paper.

### Solution

(From Unit 2, Lesson 17.)

### Problem 6

Select all the statements that must be true for any scaled copy Q of Polygon P.

A:

The side lengths are all whole numbers.

B:

The angle measures are all whole numbers.

C:

Q has exactly 1 right angle.

D:

If the scale factor between P and Q is $$\frac15$$, then each side length of P is multiplied by $$\frac15$$ to get the corresponding side length of Q.

E:

If the scale factor is 2, each angle in P is multiplied by 2 to get the corresponding angle in Q.

F:

Q has 2 acute angles and 3 obtuse angles.