# Lesson 9

### Problem 1

Find the solution(s) to each of these equations, or explain why there is no solution.

1. $$\sqrt{x+5}+7 = 10$$
2. $$\sqrt{x-2}+3=\text-2$$

### Solution

For access, consult one of our IM Certified Partners.

### Problem 2

For each equation, decide how many solutions it has and explain how you know.

1. $$(x-4)^2= 25$$
2. $$\sqrt{x-4} = 5$$
3. $$x^3 -7 = \text-20$$
4. $$6 \boldcdot \sqrt{x} = 0$$

### Solution

For access, consult one of our IM Certified Partners.

### Problem 3

Jada was solving the equation $$\sqrt{6-x}=\text-16$$. She was about to square each side, but then she realized she could give an answer without doing any algebra. What did she realize?

### Solution

For access, consult one of our IM Certified Partners.

### Problem 4

Here are the steps Tyler took to solve the equation $$\sqrt{x+3}=\text-5$$.

\begin{align} \sqrt{x+3} & =\text-5 \\ x+3 &=25 \\ x &=22 \\ \end{align}

1. Check Tyler’s answer: Is the equation true if $$x=22$$? Explain or show your reasoning.
2. What mistake did Tyler make?

### Solution

For access, consult one of our IM Certified Partners.

### Problem 5

Complete the table. Use powers of 16 in the top row and radicals or rational numbers in the bottom row.

 $$16^1$$ $$16^{\frac13}$$ $$16^{\text-1}$$ 4 1 $$\frac14$$ $$\frac{1}{16}$$

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 3, Lesson 3.)

### Problem 6

Which are the solutions to the equation $$x^3=35$$?

A:

$$\sqrt{35}$$

B:

$$\text-\sqrt{35}$$

C:

both $$\sqrt{35}$$ and $$\text-\sqrt{35}$$

D:

The equation has no solutions.

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 3, Lesson 8.)