Question

solve the equation. check your solution.
8x - (3x - 1) = 2
\\(\left\\{\frac{1}{11}\
ight\\}\\)
\\(\left\\{\frac{1}{5}\
ight\\}\\)
\\(\left\\{-\frac{1}{11}\
ight\\}\\)
\\(\left\\{-\frac{1}{5}\
ight\\}\\)

Explanation:

Step1: Remove parentheses, distribute negative

$8x - 3x + 1 = 2$

Step2: Combine like terms

$5x + 1 = 2$

Step3: Subtract 1 from both sides

$5x = 2 - 1$
$5x = 1$

Step4: Solve for x, divide by 5

$x = \frac{1}{5}$

Step5: Verify solution in original equation

Substitute $x=\frac{1}{5}$:
$8(\frac{1}{5}) - (3(\frac{1}{5}) - 1) = \frac{8}{5} - (\frac{3}{5} - \frac{5}{5}) = \frac{8}{5} - (-\frac{2}{5}) = \frac{8}{5} + \frac{2}{5} = \frac{10}{5} = 2$
Left side equals right side, solution is valid.

Answer:

$\boldsymbol{\{\frac{1}{5}\}}$ (Option B)