Solve 7|3f + 4| = 91 for f. a. –29 or 312⁄3 b. 3 or –17⁄3 c. –3 or 17⁄3 d. –312⁄3 or 29

B

Step-by-step explanation:

Given

7 | 3f + 4 | = 91 ← divide both sides by 7

| 3f + 4 | = 13

The absolute value function always returns a positive value, but the expression inside can be positive or negative. Thus there are 2 possible solutions.

Solve 3f + 4 = 13 → 3f = 13 - 4 = 9 ⇒ f = 3

Solve 3f + 4 = - 13 ⇒ 3f = - 13 - 4 = - 17 ⇒ f = -

As a check

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

f = 3 : 7| 9 + 4| = 7| 13| = 7 × 13 = 91 ← True

f = -

7 | - 17 + 4| = 7| - 13| = 7 × 13 = 91 ← True

Hence the correct solutions are B

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