Question

what is the solution to the linear equation?
$\frac{2}{3}x - \frac{1}{2}=\frac{1}{3}+\frac{5}{6}x$
$x = - 5$
$x=-\frac{1}{6}$
$x=\frac{1}{6}$
$x = 5$

Explanation:

Step1: Move x - terms to one side

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

Step2: Find a common - denominator for x - terms and constant terms

For x - terms, the common denominator of 3 and 6 is 6. $\frac{2}{3}x=\frac{4}{6}x$, so $\frac{4}{6}x-\frac{5}{6}x=\frac{4 - 5}{6}x=-\frac{1}{6}x$.
For constant terms, the common denominator of 3 and 2 is 6. $\frac{1}{3}+\frac{1}{2}=\frac{2 + 3}{6}=\frac{5}{6}$.
So the equation becomes $-\frac{1}{6}x=\frac{5}{6}$.

Step3: Solve for x

Multiply both sides of the equation by - 6. $x=\frac{5}{6}\times(-6)=-5$.

Answer:

$x = - 5$