To solve the equation [tex]\(-2x + 14 + 10x = 34\)[/tex] for [tex]\(x\)[/tex], follow these detailed steps:
1. Combine like terms:
[tex]\[
-2x + 10x + 14 = 34
\][/tex]
Combine the [tex]\(x\)[/tex] terms:
[tex]\[
(10x - 2x) + 14 = 34
\][/tex]
Simplify:
[tex]\[
8x + 14 = 34
\][/tex]
2. Isolate the term with [tex]\(x\)[/tex]:
[tex]\[
8x + 14 = 34
\][/tex]
Subtract 14 from both sides to move the constant term to the right side of the equation:
[tex]\[
8x = 34 - 14
\][/tex]
Simplify:
[tex]\[
8x = 20
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Divide both sides of the equation by 8:
[tex]\[
x = \frac{20}{8}
\][/tex]
Simplify the fraction:
[tex]\[
x = \frac{5}{2}
\][/tex]
Therefore, the solution for [tex]\(x\)[/tex] in the equation [tex]\(-2x + 14 + 10x = 34\)[/tex] is [tex]\(\frac{5}{2}\)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{x = \frac{5}{2}}
\][/tex]
