Question

solve
$4|x + 5| = 48$
a. ${-17, 5}$
b. ${-17, 7}$
c. ${-7, 17}$
d. ${7, 12}$

Explanation:

Step1: Isolate absolute value

Divide both sides by 4:
$$|x + 5| = \frac{48}{4} = 12$$

Step2: Split into two cases

Case 1: $x + 5 = 12$
Case 2: $x + 5 = -12$

Step3: Solve Case 1

Subtract 5 from both sides:
$x = 12 - 5 = 7$

Step4: Solve Case 2

Subtract 5 from both sides:
$x = -12 - 5 = -17$

Step5: Verify solutions

Substitute $x=-17$: $4|-17+5|=4|-12|=48$
Substitute $x=5$: $4|5+5|=4|10|=40$ (correction: earlier miscalculation, correct Case1: $x=12-5=7$ was wrong, correct: $|x+5|=12$ → $x+5=12$ → $x=7$? No, wait $4|7+5|=4*12=48$, $4|-17+5|=4*12=48$. Wait no, original calculation error: $\frac{48}{4}=12$, so $x+5=12$ → $x=7$, $x+5=-12$ → $x=-17$. Wait no, option A is {-17,5}, option B is {-17,7}. Recheck: $4|5+5|=4*10=40≠48$, $4|7+5|=4*12=48$. Oh! I made a typo in Step3. Correct Step3: $x=12-5=7$. So correct solution set is $\{-17,7\}$? No, wait $4|-17+5|=4*|-12|=4*12=48$, $4|7+5|=4*12=48$. So correct answer is B. $\{-17, 7\}$

Corrected Answer:

B. $\{-17, 7\}$

Step1: Isolate absolute value

Divide by 4:
$$|x + 5| = \frac{48}{4} = 12$$

Step2: Split into two equations

Positive case: $x + 5 = 12$
Negative case: $x + 5 = -12$

Step3: Solve positive case

Subtract 5:
$x = 12 - 5 = 7$

Step4: Solve negative case

Subtract 5:
$x = -12 - 5 = -17$

Step5: Validate solutions

For $x=7$: $4|7+5|=4×12=48$
For $x=-17$: $4|-17+5|=4×12=48$
Both satisfy the original equation.

Answer:

A. $\{-17, 5\}$