To find the other solution of the equation [tex]\(6 - 4|2x - 8| = -10\)[/tex], let's follow a step-by-step approach similar to Hiroto's:
1. Start with the given equation and simplify:
[tex]\[
6 - 4|2x - 8| = -10
\][/tex]
Subtract 6 from both sides:
[tex]\[
6 - 4|2x - 8| - 6 = -10 - 6
\][/tex]
Which simplifies to:
[tex]\[
-4|2x - 8| = -16
\][/tex]
2. Isolate the absolute value:
Divide both sides by -4:
[tex]\[
|2x - 8| = 4
\][/tex]
3. Consider the definition of absolute value:
The equation [tex]\( |2x - 8| = 4 \)[/tex] gives us two separate cases to consider:
[tex]\[
2x - 8 = 4 \quad \text{or} \quad 2x - 8 = -4
\][/tex]
4. Solve each equation separately for [tex]\(x\)[/tex]:
- Case 1:
[tex]\[
2x - 8 = 4
\][/tex]
Add 8 to both sides:
[tex]\[
2x = 12
\][/tex]
Divide by 2:
[tex]\[
x = 6
\][/tex]
- Case 2:
[tex]\[
2x - 8 = -4
\][/tex]
Add 8 to both sides:
[tex]\[
2x = 4
\][/tex]
Divide by 2:
[tex]\[
x = 2
\][/tex]
Since Hiroto already found the solution [tex]\( x = 6 \)[/tex], the other solution is:
[tex]\[
x = 2
\][/tex]
Thus, the other solution to the equation is:
[tex]\[
\boxed{2}
\][/tex]
