To solve the equation [tex]\(-2x + 14 + 10x = 34\)[/tex] for [tex]\(x\)[/tex], let's proceed step by step:
1. Combine like terms:
[tex]\[
-2x + 10x + 14 = 34
\][/tex]
Combine [tex]\(-2x\)[/tex] and [tex]\(10x\)[/tex]:
[tex]\[
(10x - 2x) + 14 = 34
\][/tex]
which simplifies to:
[tex]\[
8x + 14 = 34
\][/tex]
2. Isolate the term with [tex]\(x\)[/tex]:
Subtract 14 from both sides of the equation:
[tex]\[
8x + 14 - 14 = 34 - 14
\][/tex]
Simplifies to:
[tex]\[
8x = 20
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Divide both sides by 8:
[tex]\[
x = \frac{20}{8}
\][/tex]
Simplify the fraction:
[tex]\[
x = \frac{20}{8} = \frac{5}{2}
\][/tex]
Thus, the correct solution for [tex]\(x\)[/tex] is [tex]\(\frac{5}{2}\)[/tex].
The correct answer is:
[tex]\[
\boxed{B. \, x = \frac{5}{2}}
\][/tex]
