Answered

Given the function [tex]\( f(x) = 4|x - 5| + 3 \)[/tex], for what values of [tex]\( x \)[/tex] is [tex]\( f(x) = 15 \)[/tex]?

A. [tex]\( x = 2, x = 8 \)[/tex]
B. [tex]\( x = 1.5, x = 8 \)[/tex]
C. [tex]\( x = 2, x = 7.5 \)[/tex]
D. [tex]\( x = 0.5, x = 7.5 \)[/tex]



Answer :

GinnyAnswer
Let's find the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( f(x) = 15 \)[/tex] for the given function [tex]\( f(x) = 4|x - 5| + 3 \)[/tex].

1. Set up the equation:
[tex]\[ 4|x - 5| + 3 = 15 \][/tex]

2. Isolate the absolute value term:
Subtract 3 from both sides to isolate the term with the absolute value:
[tex]\[ 4|x - 5| = 12 \][/tex]

3. Solve for the absolute value:
Divide both sides by 4:
[tex]\[ |x - 5| = 3 \][/tex]

4. Rewrite the absolute value equation as two separate equations:
The absolute value equation [tex]\( |x - 5| = 3 \)[/tex] can be rewritten as two separate linear equations:
[tex]\[ x - 5 = 3 \quad \text{or} \quad x - 5 = -3 \][/tex]

5. Solve each equation for [tex]\( x \)[/tex]:

- For [tex]\( x - 5 = 3 \)[/tex]:
[tex]\[ x = 3 + 5 \][/tex]
[tex]\[ x = 8 \][/tex]

- For [tex]\( x - 5 = -3 \)[/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].

Therefore, the correct answer is:
[tex]\[ x = 2, x = 8 \][/tex]

Other Questions