Answer :
Sure! Let's solve the equation [tex]\(4|x+5| = 28\)[/tex] step by step.
1. Isolate the Absolute Value:
Start by dividing both sides of the equation by 4 to simplify the absolute value:
[tex]\[
|x+5| = \frac{28}{4} = 7
\][/tex]
2. Set Up Two Equations:
The absolute value equation [tex]\( |x+5| = 7 \)[/tex] means that:
[tex]\[
x + 5 = 7 \quad \text{or} \quad x + 5 = -7
\][/tex]
3. Solve Each Equation:
- For [tex]\( x + 5 = 7 \)[/tex]:
[tex]\[
x = 7 - 5 = 2
\][/tex]
- For [tex]\( x + 5 = -7 \)[/tex]:
[tex]\[
x = -7 - 5 = -12
\][/tex]
4. Solutions:
The solutions to the equation [tex]\(4|x+5| = 28\)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -12 \)[/tex].
So, the correct answer is C. [tex]\(x = -12\)[/tex] and [tex]\(x = 2\)[/tex].
1. Isolate the Absolute Value:
Start by dividing both sides of the equation by 4 to simplify the absolute value:
[tex]\[
|x+5| = \frac{28}{4} = 7
\][/tex]
2. Set Up Two Equations:
The absolute value equation [tex]\( |x+5| = 7 \)[/tex] means that:
[tex]\[
x + 5 = 7 \quad \text{or} \quad x + 5 = -7
\][/tex]
3. Solve Each Equation:
- For [tex]\( x + 5 = 7 \)[/tex]:
[tex]\[
x = 7 - 5 = 2
\][/tex]
- For [tex]\( x + 5 = -7 \)[/tex]:
[tex]\[
x = -7 - 5 = -12
\][/tex]
4. Solutions:
The solutions to the equation [tex]\(4|x+5| = 28\)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -12 \)[/tex].
So, the correct answer is C. [tex]\(x = -12\)[/tex] and [tex]\(x = 2\)[/tex].