Using Equations to Solve Problems | Mathematics Homework Help

A.

Read the assignment carefully and make sure you answer each part of the question or questions.

Your Assignment

The perimeter of a rectangle is 40 cm. The length is 14 cm. Let x = width of the rectangle.

Ravi says he can find the width using the equation 2(x + 14) = 40. Fran says she can find the width using the equation 2x + 28 = 40.

Answer the questions to solve the equations and to compare the steps and solutions.

1. Which of these is the most helpful first step for solving Ravi’s equation, 2(x + 14) = 40? (1 point)

Circle the best answer.

· Add 14 to both sides

· Subtract 14 from both sides

· Divide both sides by 2

· Multiply both sides by 2

2. What would your next step be? (1 point)

3. Solve Ravi’s equation, 2(x + 14) = 40, to find the width of the rectangle. Show your work. (1 point)

4. Which of these is the most helpful first step for solving Fran’s equation, 2x + 28 = 40? (1 point)

Circle the best answer.

· Multiply both sides by 2

· Subtract 28 from both sides

· Divide both sides by 2

· Add 28 to both sides

5. What would your next step be? (2 points)

6. Solve Fran’s equation, 2x + 28 = 40, to find the width of the rectangle. Show your work. (2 points)

7. The two equations have different solution steps. Do they have the same solution? Use the distributive property to show why this answer makes sense. (2 points)

B. Practice: Solving Linear Inequalities

Tyra’s family is spending the afternoon in Millersville. They plan to see a movie and then explore the town. The movie will cost the family $36, and parking costs $4 per hour.

How long will the family be able to spend in Millersville if they want to spend less than $60 and they don’t have any other expenses?

Follow the steps to answer this question.

1. Write an inequality that shows that Tyra’s family spends less than their limit. Explain how you wrote the inequality, and define any variables used. (5 points)

2. Solve your inequality. Show your work. What does your solution mean? (5 points)