Verified Answer :

7 = 0.5|x-4|- 3     add 3 to both sides: -
0.5|x-4| = 10        divide bs by 0,5:-
|x-4| = 20

either x - 4 = 20  or x - 4 = -20

this gives x = 24, x = -16

calculista

we have

\(f(x)=0.5\left|x-4\right|-3\) -----> equation A

\(f(x)=7\) -----> equation B

equate equation A and equation B

\(0.5\left|x-4\right|-3=7\)

Adds \(3\) boths sides

\(0.5\left|x-4\right|-3+3=7+3\)

\(0.5\left|x-4\right|=10\)

Multiply by \(2\) boths sides

\(\left|x-4\right|=20\)

we know that

The function absolute value has two solutions

Step 1

Find the first solution (positive case)

\(+(x-4)=20\)

Adds \(4\) boths sides

\(x-4+4=20+4\)

\(x=24\)

Step 2

Find the second solution (negative case)

\(-(x-4)=20\)

Multiply by \(-1\) boths sides

\((x-4)=-20\)

Adds \(4\) boths sides

\(x-4+4=-20+4\)

\(x=-16\)

therefore

the answer is the option B

\(x=-16, x=24\)

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