Answer :
To solve the equation [tex]\(4|x+5|=28\)[/tex], let's break it down step-by-step:
1. Divide Both Sides by 4:
[tex]\[
4|x+5| = 28
\][/tex]
Dividing each side by 4 gives:
[tex]\[
|x+5| = 7
\][/tex]
2. Consider the Definition of Absolute Value:
The absolute value equation [tex]\(|x+5| = 7\)[/tex] means there are two possible cases to consider:
- [tex]\(x + 5 = 7\)[/tex]
- [tex]\(x + 5 = -7\)[/tex]
3. Solve Each Equation Separately:
- First Case: [tex]\(x + 5 = 7\)[/tex]
[tex]\[
x = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]
- Second Case: [tex]\(x + 5 = -7\)[/tex]
[tex]\[
x = -7 - 5
\][/tex]
[tex]\[
x = -12
\][/tex]
4. Conclusion:
The solutions to the equation are [tex]\(x = 2\)[/tex] and [tex]\(x = -12\)[/tex].
From the given options, the correct answer is:
- C. [tex]\(x = -12\)[/tex] and [tex]\(x = 2\)[/tex]
1. Divide Both Sides by 4:
[tex]\[
4|x+5| = 28
\][/tex]
Dividing each side by 4 gives:
[tex]\[
|x+5| = 7
\][/tex]
2. Consider the Definition of Absolute Value:
The absolute value equation [tex]\(|x+5| = 7\)[/tex] means there are two possible cases to consider:
- [tex]\(x + 5 = 7\)[/tex]
- [tex]\(x + 5 = -7\)[/tex]
3. Solve Each Equation Separately:
- First Case: [tex]\(x + 5 = 7\)[/tex]
[tex]\[
x = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]
- Second Case: [tex]\(x + 5 = -7\)[/tex]
[tex]\[
x = -7 - 5
\][/tex]
[tex]\[
x = -12
\][/tex]
4. Conclusion:
The solutions to the equation are [tex]\(x = 2\)[/tex] and [tex]\(x = -12\)[/tex].
From the given options, the correct answer is:
- C. [tex]\(x = -12\)[/tex] and [tex]\(x = 2\)[/tex]