To solve the equation [tex]\( 10(x-1) = 8x - 2 \)[/tex] for [tex]\( x \)[/tex], follow these steps:
1. Distribute the 10 on the left-hand side:
[tex]\[
10(x - 1) = 10x - 10
\][/tex]
So the equation becomes:
[tex]\[
10x - 10 = 8x - 2
\][/tex]
2. Combine like terms involving [tex]\( x \)[/tex]:
Subtract [tex]\( 8x \)[/tex] from both sides to get all [tex]\( x \)[/tex]-terms on one side:
[tex]\[
10x - 8x - 10 = -2
\][/tex]
Simplifying this, we get:
[tex]\[
2x - 10 = -2
\][/tex]
3. Isolate the [tex]\( x \)[/tex]-term:
Add 10 to both sides to get rid of the constant term on the left side:
[tex]\[
2x - 10 + 10 = -2 + 10
\][/tex]
Simplifying this, we have:
[tex]\[
2x = 8
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
Divide both sides by 2:
[tex]\[
\frac{2x}{2} = \frac{8}{2}
\][/tex]
Simplifying this, we get:
[tex]\[
x = 4
\][/tex]
So, the value of [tex]\( x \)[/tex] that solves the equation [tex]\( 10(x-1) = 8x - 2 \)[/tex] is [tex]\( x = 4 \)[/tex].
Therefore, the correct answer is [tex]\( x = 4 \)[/tex].
