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Answer :
Let's solve the equation [tex]\( 5|x+9| = 80 \)[/tex] step by step.
1. Isolate the absolute value expression:
Divide both sides of the equation by 5:
[tex]\[
|x + 9| = \frac{80}{5} = 16
\][/tex]
2. Consider the two cases for absolute value:
The expression inside the absolute value, [tex]\( x + 9 \)[/tex], can be either positive or negative. So we'll have two cases to consider:
- Case 1: [tex]\( x + 9 = 16 \)[/tex]
- Case 2: [tex]\( x + 9 = -16 \)[/tex]
3. Solve each case:
- Case 1: [tex]\( x + 9 = 16 \)[/tex]
Subtract 9 from both sides:
[tex]\[
x = 16 - 9 = 7
\][/tex]
- Case 2: [tex]\( x + 9 = -16 \)[/tex]
Subtract 9 from both sides:
[tex]\[
x = -16 - 9 = -25
\][/tex]
4. Write the solutions:
The solutions are [tex]\( x = 7 \)[/tex] and [tex]\( x = -25 \)[/tex].
Therefore, the correct answer is:
D. [tex]\( x = -25 \)[/tex] or [tex]\( x = 7 \)[/tex]
1. Isolate the absolute value expression:
Divide both sides of the equation by 5:
[tex]\[
|x + 9| = \frac{80}{5} = 16
\][/tex]
2. Consider the two cases for absolute value:
The expression inside the absolute value, [tex]\( x + 9 \)[/tex], can be either positive or negative. So we'll have two cases to consider:
- Case 1: [tex]\( x + 9 = 16 \)[/tex]
- Case 2: [tex]\( x + 9 = -16 \)[/tex]
3. Solve each case:
- Case 1: [tex]\( x + 9 = 16 \)[/tex]
Subtract 9 from both sides:
[tex]\[
x = 16 - 9 = 7
\][/tex]
- Case 2: [tex]\( x + 9 = -16 \)[/tex]
Subtract 9 from both sides:
[tex]\[
x = -16 - 9 = -25
\][/tex]
4. Write the solutions:
The solutions are [tex]\( x = 7 \)[/tex] and [tex]\( x = -25 \)[/tex].
Therefore, the correct answer is:
D. [tex]\( x = -25 \)[/tex] or [tex]\( x = 7 \)[/tex]
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