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Hiroto solved the equation [tex]\(6-4|2x-8|=-10\)[/tex] for one solution. His work is shown below:

[tex]\[
\begin{array}{l}
6-4|2x-8|=-10 \\
-4|2x-8|=-16 \\
|2x-8|=4 \\
2x-8=4 \\
2x=12 \\
x=6
\end{array}
\][/tex]

What is the other solution?

A. [tex]\(-6\)[/tex]
B. [tex]\(-4\)[/tex]
C. [tex]\(2\)[/tex]
D. [tex]\(10\)[/tex]



Answer :

GinnyAnswer
To determine the other solution of the equation [tex]\(6 - 4|2x - 8| = -10\)[/tex], let us first rewrite the equation and follow a step-by-step solution:

Given equation:
[tex]\[6 - 4|2x - 8| = -10\][/tex]

First, isolate the absolute value expression [tex]\( |2x - 8| \)[/tex]:
[tex]\[ 6 - 4|2x - 8| = -10 \][/tex]
Subtract 6 from both sides:
[tex]\[ -4|2x - 8| = -16 \][/tex]
Divide both sides by -4:
[tex]\[ |2x - 8| = 4 \][/tex]

The absolute value equation [tex]\( |2x - 8| = 4 \)[/tex] actually represents two separate equations:
1. [tex]\( 2x - 8 = 4 \)[/tex]
2. [tex]\( 2x - 8 = -4 \)[/tex]

We will solve each equation separately.

First Equation:
[tex]\[ 2x - 8 = 4 \][/tex]
Add 8 to both sides:
[tex]\[ 2x = 12 \][/tex]
Divide by 2:
[tex]\[ x = 6 \][/tex]

Hiroto already found this solution as [tex]\( x = 6 \)[/tex].

Second Equation:
[tex]\[ 2x - 8 = -4 \][/tex]
Add 8 to both sides:
[tex]\[ 2x = 4 \][/tex]
Divide by 2:
[tex]\[ x = 2 \][/tex]

Thus, the other solution to the equation is:
[tex]\[ \boxed{2} \][/tex]

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