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What is the solution for [tex]$x$[/tex] in the equation? [tex]-2x + 14 + 10x = 34[/tex]
A. [tex]z = \frac{2}{5}[/tex] B. [tex]z = 6[/tex] C. [tex]x = \frac{5}{2}[/tex] D. [tex]z = \frac{1}{8}[/tex]
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]
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