Question

Sandra is making a sign for her chess club. Two possible designs for the base of the

3x +7
x + 3
2x - 2
sign are shown.
Is there a value of x for which the
perimeters of the figures are equal?
Show all work! Explain your reasoning.

Answer 1

The value of x that makes the perimeters of the two designs equal is x = -2.

Step-by-step explanation:

The perimeters of the two designs can be found by simplifying the expressions:

Design 1: 3x + 7

Design 2: x + 3

To find the value of x for which the perimeters are equal, we set the two expressions equal to each other:

3x + 7 = x + 3

By solving this equation for x, we can find the value that makes the perimeters equal.

Step 1: Subtract x from both sides:

2x + 7 = 3

Step 2: Subtract 7 from both sides:

2x = -4

Step 3: Divide both sides by 2:

x = -2

Therefore, the value of x that makes the perimeters of the two designs equal is x = -2.