To solve the equation [tex]\( 4|x+5|=28 \)[/tex], let's follow a step-by-step approach.
1. Isolate the absolute value expression:
[tex]\[
4|x+5| = 28
\][/tex]
Divide both sides by 4 to isolate the absolute value:
[tex]\[
|x+5| = 7
\][/tex]
2. Rewrite the absolute value equation:
The absolute value equation [tex]\( |x+5| = 7 \)[/tex] can be rewritten as two separate linear equations:
[tex]\[
x+5 = 7 \quad \text{or} \quad x+5 = -7
\][/tex]
3. Solve each linear equation:
- For [tex]\( x+5 = 7 \)[/tex]:
[tex]\[
x+5 = 7 \implies x = 7 - 5 \implies x = 2
\][/tex]
- For [tex]\( x+5 = -7 \)[/tex]:
[tex]\[
x+5 = -7 \implies x = -7 - 5 \implies x = -12
\][/tex]
4. List the solutions:
The solutions to the equation [tex]\( 4|x+5| = 28 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -12 \)[/tex].
Hence, the correct answer is:
D. [tex]\( x = -12 \)[/tex] and [tex]\( x = 2 \)[/tex]
