# Lesson 19

Solving Equations with Rational Numbers

### Problem 1

Solve.

1. $$\frac25t=6$$

2. $$\text-4.5 = a-8$$

3. $$\frac12+p= \text-3$$

4. $$12=x \boldcdot 3$$

5. $$\text-12 = \text-3y$$

### Problem 2

Match each equation to a step that will help solve the equation.

### Problem 3

1. Write an equation where a number is added to a variable, and a solution is -8.
2. Write an equation where a number is multiplied by a variable, and a solution is $$\frac {\text{-}4}{5}$$.

### Problem 4

Evaluate each expression if $$x$$ is $$\frac{2}{5}$$, $$y$$ is $$\text-4$$, and $$z$$ is -0.2.

1. $$x+y$$

2. $$2x-z$$

3. $$x+y+z$$

4. $$y \boldcdot x$$

### Solution

(From Unit 7, Lesson 18.)

### Problem 5

The markings on the number line are evenly spaced. Label the other markings on the number line.

### Solution

(From Unit 7, Lesson 14.)

### Problem 6

One night, it is $$24^\circ\text{C}$$ warmer in Tucson than it was in Minneapolis. If the temperatures in Tucson and Minneapolis are opposites, what is the temperature in Tucson?

A:

$$\text-24^\circ\text{C}$$

B:

$$\text-12^\circ\text{C}$$

C:

$$12^\circ\text{C}$$

D:

$$24^\circ\text{C}$$