1

Problem

Find a if \$| a + 2 | = | 2a + 1 |\$.

2

Step

Given that

\$| a + 2 | = | 2a + 1 |\$

3

Formula

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

4

Hint

The absolute value of a number represents its distance from zero on the number line.

5

Step

Due to the nature of absolute value, there are two possibilities:

Case 1: The expressions inside the absolute value signs are equal.

Case 2: The expressions inside the absolute value signs are opposites of each other.

6

Step

Solve Case 1: a + 2 = 2a + 1

Subtract a from both sides:
a + 2 - a = 2a + 1 - a
2 = a + 1
a = 2 - 1
a = 1

7

Step

Solve Case 2: a + 2 = -(2a + 1)

Distribute the negative: a + 2 = -2a - 1
Combine like terms: 3a = -3
Divide by 3: a = -1

8

Solution

The solutions to the equation \$| a + 2 | = | 2a + 1 |\$ are a = 1 and a = -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 = 1, -1

12

Choice-C

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

Wrong x = 1

13

Choice-D

This option is incorrect as 6 is not a solution to the given equation

Wrong x = 6

14

Answer

Option

B

15

Sumup

Please Summarize Choices