Answer :
To solve the problem:
Given the function [tex]\( f(x) = 4|x - 5| + 3 \)[/tex], we want to find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex].
1. Start with the equation:
[tex]\[
4|x - 5| + 3 = 15
\][/tex]
2. Subtract 3 from both sides to simplify the equation:
[tex]\[
4|x - 5| = 12
\][/tex]
3. Divide both sides by 4 to isolate the absolute value:
[tex]\[
|x - 5| = 3
\][/tex]
4. The absolute value equation [tex]\( |x - 5| = 3 \)[/tex] means there are two scenarios to consider:
- Scenario 1: [tex]\( x - 5 = 3 \)[/tex]
- Scenario 2: [tex]\( x - 5 = -3 \)[/tex]
5. Solve for [tex]\( x \)[/tex] in each scenario:
- For Scenario 1:
[tex]\[
x - 5 = 3
\][/tex]
Add 5 to both sides:
[tex]\[
x = 8
\][/tex]
- For Scenario 2:
[tex]\[
x - 5 = -3
\][/tex]
Add 5 to both sides:
[tex]\[
x = 2
\][/tex]
So, the values of [tex]\( x \)[/tex] for which the function [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = 2 \)[/tex]. Therefore, the correct answer is:
[tex]\( x = 2, x = 8 \)[/tex]
Given the function [tex]\( f(x) = 4|x - 5| + 3 \)[/tex], we want to find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex].
1. Start with the equation:
[tex]\[
4|x - 5| + 3 = 15
\][/tex]
2. Subtract 3 from both sides to simplify the equation:
[tex]\[
4|x - 5| = 12
\][/tex]
3. Divide both sides by 4 to isolate the absolute value:
[tex]\[
|x - 5| = 3
\][/tex]
4. The absolute value equation [tex]\( |x - 5| = 3 \)[/tex] means there are two scenarios to consider:
- Scenario 1: [tex]\( x - 5 = 3 \)[/tex]
- Scenario 2: [tex]\( x - 5 = -3 \)[/tex]
5. Solve for [tex]\( x \)[/tex] in each scenario:
- For Scenario 1:
[tex]\[
x - 5 = 3
\][/tex]
Add 5 to both sides:
[tex]\[
x = 8
\][/tex]
- For Scenario 2:
[tex]\[
x - 5 = -3
\][/tex]
Add 5 to both sides:
[tex]\[
x = 2
\][/tex]
So, the values of [tex]\( x \)[/tex] for which the function [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = 2 \)[/tex]. Therefore, the correct answer is:
[tex]\( x = 2, x = 8 \)[/tex]
