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Answer :
Sure, let's solve the given problem step-by-step:
Given the function [tex]\( f(x) = 4|x-5| + 3 \)[/tex], we need to find the values of [tex]\( x \)[/tex] such that [tex]\( f(x) = 15 \)[/tex].
Step 1: Set up the equation
[tex]\[ 4|x-5| + 3 = 15 \][/tex]
Step 2: Isolate the absolute value term
Subtract 3 from both sides:
[tex]\[ 4|x-5| = 12 \][/tex]
Step 3: Solve for the absolute value
Divide both sides by 4:
[tex]\[ |x-5| = 3 \][/tex]
Step 4: Remove the absolute value by considering both cases
Case 1:
[tex]\[ x - 5 = 3 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = 3 + 5 \][/tex]
[tex]\[ x = 8 \][/tex]
Case 2:
[tex]\[ x - 5 = -3 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = -3 + 5 \][/tex]
[tex]\[ x = 2 \][/tex]
So, the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
Thus, the correct answer is:
[tex]\[ x = 2, x = 8 \][/tex]
Given the function [tex]\( f(x) = 4|x-5| + 3 \)[/tex], we need to find the values of [tex]\( x \)[/tex] such that [tex]\( f(x) = 15 \)[/tex].
Step 1: Set up the equation
[tex]\[ 4|x-5| + 3 = 15 \][/tex]
Step 2: Isolate the absolute value term
Subtract 3 from both sides:
[tex]\[ 4|x-5| = 12 \][/tex]
Step 3: Solve for the absolute value
Divide both sides by 4:
[tex]\[ |x-5| = 3 \][/tex]
Step 4: Remove the absolute value by considering both cases
Case 1:
[tex]\[ x - 5 = 3 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = 3 + 5 \][/tex]
[tex]\[ x = 8 \][/tex]
Case 2:
[tex]\[ x - 5 = -3 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = -3 + 5 \][/tex]
[tex]\[ x = 2 \][/tex]
So, the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
Thus, the correct answer is:
[tex]\[ x = 2, x = 8 \][/tex]
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