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Answer :
To find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] where [tex]\( f(x)=4|x-5|+3 \)[/tex], let's solve the equation step-by-step.
1. Set the equation:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
2. Isolate the absolute value:
[tex]\[
4|x-5| = 15 - 3
\][/tex]
[tex]\[
4|x-5| = 12
\][/tex]
3. Divide both sides by 4:
[tex]\[
|x-5| = 3
\][/tex]
4. Solve the absolute value equation:
The expression [tex]\(|x-5| = 3\)[/tex] implies two separate equations:
[tex]\[
x - 5 = 3 \quad \text{and} \quad x - 5 = -3
\][/tex]
5. Solve each equation:
- For [tex]\( x - 5 = 3 \)[/tex]:
[tex]\[
x = 3 + 5 = 8
\][/tex]
- For [tex]\( x - 5 = -3 \)[/tex]:
[tex]\[
x = -3 + 5 = 2
\][/tex]
6. Conclusion:
The values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
Therefore, the correct answer is [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
1. Set the equation:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
2. Isolate the absolute value:
[tex]\[
4|x-5| = 15 - 3
\][/tex]
[tex]\[
4|x-5| = 12
\][/tex]
3. Divide both sides by 4:
[tex]\[
|x-5| = 3
\][/tex]
4. Solve the absolute value equation:
The expression [tex]\(|x-5| = 3\)[/tex] implies two separate equations:
[tex]\[
x - 5 = 3 \quad \text{and} \quad x - 5 = -3
\][/tex]
5. Solve each equation:
- For [tex]\( x - 5 = 3 \)[/tex]:
[tex]\[
x = 3 + 5 = 8
\][/tex]
- For [tex]\( x - 5 = -3 \)[/tex]:
[tex]\[
x = -3 + 5 = 2
\][/tex]
6. Conclusion:
The values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
Therefore, the correct answer is [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
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