Question

question 2a
all answers should be in simplest form. use dne if there is no solution.

1. solve:

a. $|x + 8| - 5 = 2$
b. $\frac{|7x + 4|}{8} = 3$
c. $3|-2x + 6| = -18$

Explanation:

Part a

Step1: Isolate the absolute value

Add 5 to both sides.
$|x+8| - 5 + 5 = 2 + 5$
$|x+8| = 7$

Step2: Split into two cases

Case 1: $x+8 = 7$; Case 2: $x+8 = -7$

Step3: Solve Case 1

Subtract 8 from both sides.
$x = 7 - 8$
$x = -1$

Step4: Solve Case 2

Subtract 8 from both sides.
$x = -7 - 8$
$x = -15$

Part b

Step1: Isolate the absolute value

Multiply both sides by 8.
$8 \times \frac{|7x+4|}{8} = 3 \times 8$
$|7x+4| = 24$

Step2: Split into two cases

Case 1: $7x+4 = 24$; Case 2: $7x+4 = -24$

Step3: Solve Case 1

Subtract 4, then divide by 7.
$7x = 24 - 4$
$7x = 20$
$x = \frac{20}{7}$

Step4: Solve Case 2

Subtract 4, then divide by 7.
$7x = -24 - 4$
$7x = -28$
$x = -4$

Part c

Step1: Isolate the absolute value

Divide both sides by 3.
$\frac{3|-2x+6|}{3} = \frac{-18}{3}$
$|-2x+6| = -6$

Step2: Analyze absolute value rule

Absolute value cannot be negative.
No solution exists.

Answer:

a. $x = -1$ or $x = -15$
b. $x = \frac{20}{7}$ or $x = -4$
c. DNE