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Answer :
Let's solve the problem step-by-step:
We are given the function [tex]\( f(x) = 4|x - 5| + 3 \)[/tex] and need to find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex].
1. Set the Equation:
Start by setting the function equal to 15:
[tex]\[
4|x - 5| + 3 = 15
\][/tex]
2. Isolate the Absolute Value:
Subtract 3 from both sides to isolate the term with the absolute value:
[tex]\[
4|x - 5| = 15 - 3
\][/tex]
[tex]\[
4|x - 5| = 12
\][/tex]
3. Solve for the Absolute Value:
Divide both sides by 4 to solve for the absolute value:
[tex]\[
|x - 5| = \frac{12}{4}
\][/tex]
[tex]\[
|x - 5| = 3
\][/tex]
4. Solve the Absolute Value Equation:
The equation [tex]\( |x - 5| = 3 \)[/tex] implies two scenarios:
- [tex]\( x - 5 = 3 \)[/tex]
- [tex]\( x - 5 = -3 \)[/tex]
Solve each equation for [tex]\( x \)[/tex]:
- For [tex]\( x - 5 = 3 \)[/tex]:
[tex]\[
x = 5 + 3 = 8
\][/tex]
- For [tex]\( x - 5 = -3 \)[/tex]:
[tex]\[
x = 5 - 3 = 2
\][/tex]
5. Conclusion:
Thus, the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = 2 \)[/tex].
Therefore, the answer is [tex]\( x = 8 \)[/tex] and [tex]\( x = 2 \)[/tex].
We are given the function [tex]\( f(x) = 4|x - 5| + 3 \)[/tex] and need to find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex].
1. Set the Equation:
Start by setting the function equal to 15:
[tex]\[
4|x - 5| + 3 = 15
\][/tex]
2. Isolate the Absolute Value:
Subtract 3 from both sides to isolate the term with the absolute value:
[tex]\[
4|x - 5| = 15 - 3
\][/tex]
[tex]\[
4|x - 5| = 12
\][/tex]
3. Solve for the Absolute Value:
Divide both sides by 4 to solve for the absolute value:
[tex]\[
|x - 5| = \frac{12}{4}
\][/tex]
[tex]\[
|x - 5| = 3
\][/tex]
4. Solve the Absolute Value Equation:
The equation [tex]\( |x - 5| = 3 \)[/tex] implies two scenarios:
- [tex]\( x - 5 = 3 \)[/tex]
- [tex]\( x - 5 = -3 \)[/tex]
Solve each equation for [tex]\( x \)[/tex]:
- For [tex]\( x - 5 = 3 \)[/tex]:
[tex]\[
x = 5 + 3 = 8
\][/tex]
- For [tex]\( x - 5 = -3 \)[/tex]:
[tex]\[
x = 5 - 3 = 2
\][/tex]
5. Conclusion:
Thus, the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = 2 \)[/tex].
Therefore, the answer is [tex]\( x = 8 \)[/tex] and [tex]\( x = 2 \)[/tex].
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Rewritten by : Jeany
