Answer :
To solve the equation [tex]\(4|x+5|=28\)[/tex], we can follow these steps:
1. Divide Both Sides by 4: Start by simplifying the equation to isolate the absolute value expression. Divide both sides by 4:
[tex]\[
|x+5| = \frac{28}{4} = 7
\][/tex]
2. Consider the Two Cases of Absolute Value: The equation [tex]\(|x+5| = 7\)[/tex] implies two possibilities because the absolute value of a number is its distance from zero on the number line. So, we have:
- Case 1: [tex]\(x + 5 = 7\)[/tex]
- Case 2: [tex]\(x + 5 = -7\)[/tex]
3. Solve Each Case Separately:
- Case 1: [tex]\(x + 5 = 7\)[/tex]
[tex]\[
x = 7 - 5 = 2
\][/tex]
- Case 2: [tex]\(x + 5 = -7\)[/tex]
[tex]\[
x = -7 - 5 = -12
\][/tex]
4. Conclusion: The solutions to the equation [tex]\(4|x+5|=28\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = -12\)[/tex].
Therefore, the correct choice among the given options is:
A. [tex]\(x = -12\)[/tex] and [tex]\(x = 2\)[/tex]
1. Divide Both Sides by 4: Start by simplifying the equation to isolate the absolute value expression. Divide both sides by 4:
[tex]\[
|x+5| = \frac{28}{4} = 7
\][/tex]
2. Consider the Two Cases of Absolute Value: The equation [tex]\(|x+5| = 7\)[/tex] implies two possibilities because the absolute value of a number is its distance from zero on the number line. So, we have:
- Case 1: [tex]\(x + 5 = 7\)[/tex]
- Case 2: [tex]\(x + 5 = -7\)[/tex]
3. Solve Each Case Separately:
- Case 1: [tex]\(x + 5 = 7\)[/tex]
[tex]\[
x = 7 - 5 = 2
\][/tex]
- Case 2: [tex]\(x + 5 = -7\)[/tex]
[tex]\[
x = -7 - 5 = -12
\][/tex]
4. Conclusion: The solutions to the equation [tex]\(4|x+5|=28\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = -12\)[/tex].
Therefore, the correct choice among the given options is:
A. [tex]\(x = -12\)[/tex] and [tex]\(x = 2\)[/tex]