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]
