# Lesson 19

Queuing on the Number Line

• Let’s use number line to reason about inequalities.

### 19.1: Notice and Wonder: Shaded Number Line

What do you notice? What do you wonder?

$$4>x$$

### 19.2: Pick a Number

For each expression, pick a number you would like to evaluate, and tell whether it makes the inequality true. Be prepared to explain what made you choose your number.

1. $$\frac43y+10>19$$
1. Pick a number you would like to test in place of $$y$$: -1, 0, 1, 3, 4, or 5. Explain why you chose your number.

2. Does your number make the inequality true?

3. What is a different number that is definitely a solution? How do you know?

4. What is a different number that is definitely not a solution? How do you know?

2. $$2.954x-14.287<13.89$$
1. Pick a number you would like to test in place of $$x$$: -1, -0.5, 0, 0.5, 1, 3, 10, or 1,000. Explain why you chose your number.

2. Does your number make the inequality true?

3. What is a different number that is definitely a solution? How do you know?

4. What is a different number that is definitely not a solution? How do you know?

3. $$10-3y<5$$
1. Pick a number you would like to test in place of $$y$$: -100, -3, -1, 0,$$\frac13$$, $$\frac53$$, 33, or 100. Explain why you chose your number.

2. Does your number make the inequality true?

3. What is a different number that is definitely a solution? How do you know?

4. What is a different number that is definitely not a solution? How do you know?

4. $$\frac{10x}{4} > \frac{3x}{5}$$
1. Pick a number you would like to test in place of $$x$$: -10, -5, -4, 0, 4, 5, 10, or 20. Explain why you chose your number.

2. Does your number make the inequality true?

3. What is a different number that is definitely a solution? How do you know?

4. What is a different number that is definitely not a solution? How do you know?

### 19.3: Matching Words and Symbols

For each inequality, write 3 values that make the inequality true, write 3 values that make it false, and choose a verbal description that matches the inequality.

1. $$x > 13.5$$
1. Three values that make it true:
2. Three values that make it false:
3. Which verbal description best matches the inequality?
1. $$x$$ is less than 13.5
2. $$x$$ is greater than 13.5
3. 13.5 is greater than $$x$$
2. $$\text- 27 < x$$
1. Three values that make it true:
2. Three values that make it false:
3. Which verbal description best matches the inequality?
1. $$x$$ is less than -27
2. $$x$$ is greater than -27
3. -27 is greater than $$x$$
3. $$x \geq \frac12$$ and $$x \leq 2.75$$
1. Three values that make it true:
2. Three values that make it false:
3. Which verbal description best matches the inequality?
1. $$x$$ is between $$\frac12$$ and 2.75
2. 2.75 is less than $$x$$ is less than $$\frac12$$
3. $$x$$ is greater than $$\frac12$$
4. $$x\geq \text-\frac{19}{4}$$ and $$x \leq \frac12$$
1. Three values that make it true:
2. Three values that make it false:
3. Which verbal description best matches the inequality?
1. $$x$$ is between $$\frac12$$ and $$\text{-}\frac{19}{4}$$
2. $$x$$ is less than $$\text-\frac{19}{4}$$
3. $$x$$ is between $$\text-\frac{19}{4}$$ and $$\frac12$$