Solving Two- Step Equations

Question

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

Ravi says he can find the width using the equation 2(× + 14)= 40.

Fran says she can find the width using the equation 2x + 28 = 40.

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

A. Add 14 to both sides

B. Subtract 14 from both sides

C. Divide both sides by 2

D. 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 the work.

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

A. Multiply byoth sides by 2

B. Subtract 28 from both sides

C. Divide both sides by 2

D. 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 the work.

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

Answer 1

1.) C

First goal is to deal with the multiplication of 2 outside the parenthesis by dividing both sides by 2.

2.) Subtract 14 from both sides.

This is to get the x by itself on the left.

3.)

2 (x + 14) = 40

*Divide by 2 on both sides*

x + 14 = 20

*Subtract 14 from both sides to get x by itself on the left*

x = 6.

4.) B

This will isolate the 2x for the next step.

5.) Divide by 2 on both sides to get x by itself.

6.)

2x + 28 = 40

*Subtract 28 from both sides to get 2x by itself on the left*

2x = 12

*Divide by 2 on both sides to solve for x*

x = 6.

7.) In Ravi's equation, we can distribute the 2 to both the x and 14 inside the parenthesis. This will result in 2x + 28 which is the same as Fran's equation. The equations have different starting points but lead to the same answer in the end.