1

Problem

Solve for x \$ | x + 3 | = | x + 9 | \$.

2

Step

Given equation:

\$ | x + 3 | = | x + 9 | \$

3

Formula

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

4

Hint

Equate the expression x + 3 and the opposite of x + 9.

5

Step

Write related linear equation

x + 3 = - (x + 9)

6

Step

Using distributive Property

x + 3 = - x - 9

7

Step

Add x to each side

2x + 3 = - 9

8

Step

Subtract 3 from each side

2x = −12

9

Step

Divide each side by 2

x = - 6

10

Hint

Equate the expression x + 3 and x + 9.

11

Step

Write related linear equation

x + 3 = x + 9

12

Step

Subtract 3 from each side

x = x + 6

13

Step

Subtract x from each side

x - x = x + 6 - x

0 = 6

14

Solution

which is a false statement. So, the original equation has only one solution and is -6.

15

Sumup

Please Summarize Problem, Hint, Clue, Formula and Steps

Choices

16

Choice-A

This option is correct as it matches the calculated solution. It represents the exact value of x that satisfies the equation

Correct x = -6

17

Choice-B

This option is incorrect. It suggests a different value for x, which does not satisfy the original equation

Wrong x = 6

18

Choice-C

This option is incorrect. It proposes a value for x that is not a solution to the equation

Wrong x = -1

19

Choice-D

This option is incorrect. It suggests a value for x that does not fulfill the conditions of the equation

Wrong x = 1

20

Answer

Option

A

21

Sumup

Please Summarize Choices