Sure! Let's solve the equation step-by-step:
The given equation is:
[tex]\[
-2x + 14 + 10x = 34
\][/tex]
Step 1: Combine the like terms on the left side of the equation.
[tex]\[
-2x + 10x = 8x
\][/tex]
So the equation simplifies to:
[tex]\[
8x + 14 = 34
\][/tex]
Step 2: Subtract 14 from both sides to isolate the term involving [tex]\( x \)[/tex].
[tex]\[
8x + 14 - 14 = 34 - 14
\][/tex]
This simplifies to:
[tex]\[
8x = 20
\][/tex]
Step 3: Divide both sides by 8 to solve for [tex]\( x \)[/tex].
[tex]\[
x = \frac{20}{8}
\][/tex]
Simplify the fraction:
[tex]\[
x = \frac{5}{2}
\][/tex]
So the solution for [tex]\( x \)[/tex] is:
[tex]\[
x = \frac{5}{2}
\][/tex]
The correct answer is:
C. [tex]\( x = \frac{5}{2} \)[/tex]
