Answer :
Sure! Let's solve the given function step-by-step.
Given the function:
[tex]\[ f(x) = 4|x - 5| + 3 \][/tex]
We need to find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex].
First, set the function equal to 15:
[tex]\[ 4|x - 5| + 3 = 15 \][/tex]
Subtract 3 from both sides to isolate the absolute value term:
[tex]\[ 4|x - 5| = 12 \][/tex]
Divide both sides by 4 to further isolate the absolute value:
[tex]\[ |x - 5| = 3 \][/tex]
The absolute value equation [tex]\( |x - 5| = 3 \)[/tex] means that [tex]\( x - 5 \)[/tex] can be either 3 or -3. Therefore, we set up two separate equations:
1. [tex]\( x - 5 = 3 \)[/tex]
2. [tex]\( x - 5 = -3 \)[/tex]
Solve each equation separately:
1. [tex]\( x - 5 = 3 \)[/tex]
[tex]\[ x = 3 + 5 \][/tex]
[tex]\[ x = 8 \][/tex]
2. [tex]\( x - 5 = -3 \)[/tex]
[tex]\[ x = -3 + 5 \][/tex]
[tex]\[ x = 2 \][/tex]
So, the solutions are:
[tex]\[ x = 2 \][/tex]
[tex]\[ x = 8 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{x = 2, x = 8} \][/tex]
Given the function:
[tex]\[ f(x) = 4|x - 5| + 3 \][/tex]
We need to find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex].
First, set the function equal to 15:
[tex]\[ 4|x - 5| + 3 = 15 \][/tex]
Subtract 3 from both sides to isolate the absolute value term:
[tex]\[ 4|x - 5| = 12 \][/tex]
Divide both sides by 4 to further isolate the absolute value:
[tex]\[ |x - 5| = 3 \][/tex]
The absolute value equation [tex]\( |x - 5| = 3 \)[/tex] means that [tex]\( x - 5 \)[/tex] can be either 3 or -3. Therefore, we set up two separate equations:
1. [tex]\( x - 5 = 3 \)[/tex]
2. [tex]\( x - 5 = -3 \)[/tex]
Solve each equation separately:
1. [tex]\( x - 5 = 3 \)[/tex]
[tex]\[ x = 3 + 5 \][/tex]
[tex]\[ x = 8 \][/tex]
2. [tex]\( x - 5 = -3 \)[/tex]
[tex]\[ x = -3 + 5 \][/tex]
[tex]\[ x = 2 \][/tex]
So, the solutions are:
[tex]\[ x = 2 \][/tex]
[tex]\[ x = 8 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{x = 2, x = 8} \][/tex]