1

Problem

Solve for x : \$\∣ x − 7 \∣ = 8\$.

2

Step

Given equation

\$\∣ x − 7 \∣ = 8\$

3

Formula

\$\∣a\∣ = b\$ implies a = b or a = −b.

4

Step

Since the distance from x to 7 is 8, there are two possibilities:

x - 7 = 8
x - 7 = - 8

5

Clue

Apply the property of absolute value to set up two equations. Solve each equation separately.

6

Step

Solve the First Equation by adding 7 to both sides:

x - 7 = 8
x - 7 + 7 = 8 + 7
x = 15

7

Step

Solve the second Equation by adding 7 to both sides:

x - 7 = - 8
x - 7 + 7 = - 8 + 7
x = - 1

8

Solution

The solutions to the equation \$| x - 7 | = 8\$ are x = 15 and x = -1.

9

Sumup

Please Summarize Problem, Hint, Clue, Formula and Steps

Choices

10

Choice-A

This option is incorrect because it only includes one of the solutions

Wrong x = -1

11

Choice-B

This option is correct because it includes both solutions to the equation

Correct x = 15, -1

12

Choice-C

This option is incorrect because it only includes one of the solutions

Wrong x = 15

13

Choice-D

This option is incorrect because one of the solutions is incorrect

Wrong x = 15, 1

14

Answer

Option

B

15

Sumup

Please Summarize Choices