Answer :
Sure, let's solve the equation [tex]\( 4|x+5|=28 \)[/tex] step-by-step.
1. Isolate the absolute value expression:
The given equation is [tex]\( 4|x+5|=28 \)[/tex]. First, divide both sides of the equation by 4:
[tex]\[
|x + 5| = \frac{28}{4}
\][/tex]
[tex]\[
|x + 5| = 7
\][/tex]
2. Set up two separate equations:
The absolute value of a number means that the number inside can be equal to 7 or -7. So we set up two equations:
[tex]\[
x + 5 = 7
\][/tex]
[tex]\[
x + 5 = -7
\][/tex]
3. Solve each equation:
- For the first equation [tex]\( x + 5 = 7 \)[/tex]:
[tex]\[
x = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]
- For the second equation [tex]\( x + 5 = -7 \)[/tex]:
[tex]\[
x = -7 - 5
\][/tex]
[tex]\[
x = -12
\][/tex]
4. Write the solutions:
The solutions to the equation [tex]\( 4|x+5|=28 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -12 \)[/tex].
Therefore, the correct answer is [tex]\(\boxed{B. \, x=-12 \text{ and } x=2}\)[/tex].
1. Isolate the absolute value expression:
The given equation is [tex]\( 4|x+5|=28 \)[/tex]. First, divide both sides of the equation by 4:
[tex]\[
|x + 5| = \frac{28}{4}
\][/tex]
[tex]\[
|x + 5| = 7
\][/tex]
2. Set up two separate equations:
The absolute value of a number means that the number inside can be equal to 7 or -7. So we set up two equations:
[tex]\[
x + 5 = 7
\][/tex]
[tex]\[
x + 5 = -7
\][/tex]
3. Solve each equation:
- For the first equation [tex]\( x + 5 = 7 \)[/tex]:
[tex]\[
x = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]
- For the second equation [tex]\( x + 5 = -7 \)[/tex]:
[tex]\[
x = -7 - 5
\][/tex]
[tex]\[
x = -12
\][/tex]
4. Write the solutions:
The solutions to the equation [tex]\( 4|x+5|=28 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -12 \)[/tex].
Therefore, the correct answer is [tex]\(\boxed{B. \, x=-12 \text{ and } x=2}\)[/tex].