Question

select the correct answer.
what is the solution for x in the equation?
-2x + 14 + 10x = 34
a. $x = \frac{1}{8}$
b. $x = 6$
c. $x = \frac{2}{5}$
d. $x = \frac{5}{2}$

Explanation:

Step1: Combine like terms

Combine the \(x\)-terms: \(-2x + 10x = 8x\). So the equation becomes \(8x + 14 = 34\).

Step2: Subtract 14 from both sides

Subtract 14 from each side: \(8x + 14 - 14 = 34 - 14\), which simplifies to \(8x = 20\).

Step3: Divide by 8

Divide both sides by 8: \(x=\frac{20}{8}=\frac{5}{2}\). Wait, no, wait, let's check again. Wait, 34 -14 is 20? Wait, no, 34 -14 is 20? Wait, 34 -14 is 20? Wait, 14 + 10x -2x =34, so 8x +14=34. Subtract 14: 8x=20? Wait, 34-14 is 20? Wait, 34-14 is 20? Wait, 14 + 20 is 34? Yes. Then 8x=20? Wait, no, wait, 8x=20? Then x=20/8=5/2? But let's check the options. Option D is \(x=\frac{5}{2}\). Wait, but let's re - do the steps carefully.

Wait, original equation: \(-2x + 14 + 10x = 34\)

Combine like terms: \((-2x + 10x)+14 = 34\) → \(8x+14 = 34\)

Subtract 14 from both sides: \(8x=34 - 14\) → \(8x = 20\)

Divide both sides by 8: \(x=\frac{20}{8}=\frac{5}{2}\)

Answer:

D. \(x=\frac{5}{2}\)