Lesson 19

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.

A:

\(5x=0.4\)

B:

\(\frac{x}{5}=8\)

C:

\(3=\frac {\text{-}x}{5}\)

D:

\(7=\text-5x\)

1:

Multiply each side by 5.

2:

Multiply each side by -5.

3:

Multiply each side by \(\frac15\).

4:

Multiply each side by \(\frac {\text{-}1}{5}\).

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. \(y \boldcdot x\)

(From Unit 7, Lesson 18.)

Problem 5

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

A blank number line with 9 evenly spaced tick marks. Starting on the left, the fourth tick mark is labeled negative 30, the fifth tick mark is labeled 0, and the ninth tick mark is labeled 45.
(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:

\(24^\circ\text{C}\)

(From Unit 7, Lesson 2.)