Answer :
Sure! Let's solve the equation [tex]\( 4|x+5| = 28 \)[/tex] step by step.
1. Isolate the absolute value expression:
[tex]\[
4|x+5| = 28
\][/tex]
Divide both sides of the equation by 4 to simplify:
[tex]\[
|x+5| = \frac{28}{4} = 7
\][/tex]
2. Set up the two possible equations:
Remember, the absolute value of [tex]\( x+5 \)[/tex] can be either positive or negative:
[tex]\[
x + 5 = 7 \quad \text{or} \quad x + 5 = -7
\][/tex]
3. Solve each equation separately:
- For [tex]\( x + 5 = 7 \)[/tex]:
[tex]\[
x + 5 = 7
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]
- For [tex]\( x + 5 = -7 \)[/tex]:
[tex]\[
x + 5 = -7
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -7 - 5
\][/tex]
[tex]\[
x = -12
\][/tex]
4. Write down the solutions:
The solutions to the equation [tex]\( 4|x+5| = 28 \)[/tex] are:
[tex]\[
x = 2 \quad \text{and} \quad x = -12
\][/tex]
Therefore, the correct answer is:
D. [tex]\( x = -12 \)[/tex] and [tex]\( x = 2 \)[/tex]
1. Isolate the absolute value expression:
[tex]\[
4|x+5| = 28
\][/tex]
Divide both sides of the equation by 4 to simplify:
[tex]\[
|x+5| = \frac{28}{4} = 7
\][/tex]
2. Set up the two possible equations:
Remember, the absolute value of [tex]\( x+5 \)[/tex] can be either positive or negative:
[tex]\[
x + 5 = 7 \quad \text{or} \quad x + 5 = -7
\][/tex]
3. Solve each equation separately:
- For [tex]\( x + 5 = 7 \)[/tex]:
[tex]\[
x + 5 = 7
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]
- For [tex]\( x + 5 = -7 \)[/tex]:
[tex]\[
x + 5 = -7
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -7 - 5
\][/tex]
[tex]\[
x = -12
\][/tex]
4. Write down the solutions:
The solutions to the equation [tex]\( 4|x+5| = 28 \)[/tex] are:
[tex]\[
x = 2 \quad \text{and} \quad x = -12
\][/tex]
Therefore, the correct answer is:
D. [tex]\( x = -12 \)[/tex] and [tex]\( x = 2 \)[/tex]