Question

solve the equation.
-3x + 1 + 10x = x + 4
\\(\bigcirc\\) \\(x = \frac{1}{2}\\)
\\(\bigcirc\\) \\(x = \frac{5}{6}\\)
\\(\bigcirc\\) \\(x = 12\\)
\\(\bigcirc\\) \\(x = 18\\)

Explanation:

Step1: Combine like terms on the left side

Combine the \(x\)-terms: \(-3x + 10x = 7x\), so the equation becomes \(7x + 1 = x + 4\).

Step2: Subtract \(x\) from both sides

Subtract \(x\) from each side: \(7x - x + 1 = x - x + 4\), which simplifies to \(6x + 1 = 4\).

Step3: Subtract 1 from both sides

Subtract 1 from each side: \(6x + 1 - 1 = 4 - 1\), resulting in \(6x = 3\).

Step4: Divide both sides by 6

Divide each side by 6: \(x = \frac{3}{6}\), and simplify the fraction to \(x = \frac{1}{2}\).

Answer:

\(x = \frac{1}{2}\) (corresponding to the option \(x = \frac{1}{2}\))