Question

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? 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?

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

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

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

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.

Answer 1

Explanation:

\1. Divide both sides by 2

2(x+14) = 40

x+14 = 20

2. Isolate the x term by subtracting 14 from both sides

3. x = 6. The width of the triangle is 6 cm.

4. Isolate the x term by subtracting 28 from both sides

2x + 28 = 40

2x = 12

5. Divide both sides by 2

6. x = 6

7. The two equations have the same solution, because by the distributive rule, 2(x+14) = 2x+28.

Answer 2

Explanation:

1. Divide both sides by 2

2(x+14) = 40

x+14 = 20

2. Isolate the x term by subtracting 14 from both sides

3. x = 6. The width of the triangle is 6 cm.

4. Isolate the x term by subtracting 28 from both sides

2x + 28 = 40

2x = 12

5. Divide both sides by 2

6. x = 6

7. The two equations have the same solution, because by the distributive rule, 2(x+14) = 2x+28.