# Lesson 15

Solving Equations with Rational Numbers

Let’s solve equations that include negative values.

### 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

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. $$y \boldcdot x$$

(From Unit 5, Lesson 13.)

### Problem 4

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 5

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

1. DeepSea Challenger’s descent was a change in depth of $$(\text-4)$$ feet per second. We can use the equation $$y=\text-4x$$ to model this relationship, where $$y$$ is the depth and $$x$$ is the time in seconds that have passed. How many seconds does this model suggest it would take for DeepSea Challenger to reach the bottom?
3. The ascent can be modeled by a different proportional relationship $$y=kx$$. What is the value of k in this case?