To solve the equation [tex]\(5x - 6 = 3x + 10\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Move the terms involving [tex]\(x\)[/tex] to one side of the equation:
Subtract [tex]\(3x\)[/tex] from both sides to collect all [tex]\(x\)[/tex]-terms on one side:
[tex]\[
5x - 3x - 6 = 10
\][/tex]
Simplifying this, we get:
[tex]\[
2x - 6 = 10
\][/tex]
2. Isolate the [tex]\(x\)[/tex]-term:
Add 6 to both sides of the equation to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
2x - 6 + 6 = 10 + 6
\][/tex]
Simplifying this, we get:
[tex]\[
2x = 16
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Divide both sides of the equation by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{16}{2}
\][/tex]
Simplifying this, we get:
[tex]\[
x = 8
\][/tex]
Thus, the solution to the equation [tex]\(5x - 6 = 3x + 10\)[/tex] is [tex]\(x = 8\)[/tex].
So, the correct answer is:
[tex]\[ x = 8 \][/tex]
