Question

solve for x.
$3x - 5 + \frac{1}{2} = \frac{2x + 5}{6}$

Explanation:

Step1: Eliminate the denominator

Multiply both sides of the equation by 6 to get rid of the fraction on the right side. So we have \(6\times(3x - 5+\frac{1}{2})=6\times\frac{2x + 5}{6}\). Simplifying both sides, the left side becomes \(6\times3x-6\times5 + 6\times\frac{1}{2}\) and the right side simplifies to \(2x + 5\). Calculating each term: \(18x-30 + 3=2x + 5\).

Step2: Simplify the left side

Combine like terms on the left side: \(18x-27 = 2x+5\).

Step3: Move variable terms to one side

Subtract \(2x\) from both sides: \(18x-2x-27=2x-2x + 5\), which simplifies to \(16x-27 = 5\).

Step4: Move constant terms to the other side

Add 27 to both sides: \(16x-27 + 27=5 + 27\), so \(16x=32\).

Step5: Solve for x

Divide both sides by 16: \(x=\frac{32}{16}=2\).

Answer:

\(x = 2\)