To solve the equation [tex]\( 10x - 2(x + 5) = 4x - 2 \)[/tex], follow these steps:
1. Distribute the -2 through the [tex]\( (x + 5) \)[/tex] term:
[tex]\[
10x - 2(x + 5) = 10x - 2x - 10
\][/tex]
2. Simplify the left side of the equation by combining like terms:
[tex]\[
10x - 2x - 10 = 8x - 10
\][/tex]
So now the equation is:
[tex]\[
8x - 10 = 4x - 2
\][/tex]
3. Move the terms involving [tex]\( x \)[/tex] to one side of the equation and the constant terms to the other side. Start by subtracting [tex]\( 4x \)[/tex] from both sides:
[tex]\[
8x - 4x - 10 = 4x - 4x - 2
\][/tex]
Simplified, this becomes:
[tex]\[
4x - 10 = -2
\][/tex]
4. Add 10 to both sides to isolate the [tex]\( 4x \)[/tex] term:
[tex]\[
4x - 10 + 10 = -2 + 10
\][/tex]
Simplified, this becomes:
[tex]\[
4x = 8
\][/tex]
5. Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{8}{4}
\][/tex]
Simplified, this gives:
[tex]\[
x = 2
\][/tex]
Therefore, the solution to the equation [tex]\( 10x - 2(x + 5) = 4x - 2 \)[/tex] is:
[tex]\[
x = 2
\][/tex]
