1

Problem

Solve the equation containing absolute value: \$2/3|r + 6 | - 7 = 9\$.

2

Step

The given equation is

\$2/3|r + 6 | - 7 = 9\$

3

Step

Move constant term 7 to left side and then simplify

\$2/3 | r + 6| = 9 + 7 \$

\$ 2/3 | r + 6| = 16\$

4

Step

Multiply both sides by \$3/2\$​ to clear the fraction and then simplify it:

\$ 2/3 times 3/2 | r + 6| = 16 times 3/2\$

\$|r + 6| = \cancel(48)^24 / \cancel(2)\$

\$|r + 6| = 24\$

5

Formula

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

6

Hint

Set up two separate equations based on the definition of absolute value: r + 6 = 24 or r + 6 = - 24.

7

Step

Solve r + 6 = 24 equation separately and then solve for r value:

r + 6 = 24

r = 24 - 6

r = 18

8

Step

Solve r + 6 = - 24 equation separately and then solve for r value:

r + 6 = - 24

r = - 24 - 6

r = - 30

9

Solution

The solutions to the equation \$2/3|r + 6 | - 7 = 9\$ are: r = 18 and r = - 30.

10

Sumup

Please Summarize Problem, Hint, Clue, Formula and Steps

Choices

11

Choice-A

Substituting these values into the equation doesn’t satisfy the original equation, so they are incorrect

Wrong r = -18 and r = -30

12

Choice-B

Option B lists r = 81 and r = - 30. While r = - 30 is indeed a solution, r = 81 does not satisfy the equation

Wrong r = 81 and r = -30

13

Choice-C

Substituting these values into the equation doesn’t satisfy the original equation, so option C is wrong

Wrong r = - 81 and r = - 30

14

Choice-D

Substituting these values into the equation satisfies the original equation, so they are correct

Correct r = 18 and r = - 30

15

Answer

Option

D

16

Sumup

Please Summarize Choices