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

Explanation:

Step1: Move x - terms to one side

Subtract $\frac{5}{6}x$ from both sides and add $\frac{1}{2}$ to both sides: $\frac{2}{3}x-\frac{5}{6}x=\frac{1}{3}+\frac{1}{2}$

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

For x - terms, the common denominator of 3 and 6 is 6. For constant terms, the common denominator of 3 and 2 is 6. $\frac{2\times2}{3\times2}x-\frac{5}{6}x=\frac{1\times2}{3\times2}+\frac{1\times3}{2\times3}$ $\frac{4}{6}x-\frac{5}{6}x=\frac{2}{6}+\frac{3}{6}$

Step3: Simplify both sides

On the left - hand side: $\frac{4}{6}x-\frac{5}{6}x=\frac{4x - 5x}{6}=-\frac{1}{6}x$. On the right - hand side: $\frac{2}{6}+\frac{3}{6}=\frac{2 + 3}{6}=\frac{5}{6}$. So, $-\frac{1}{6}x=\frac{5}{6}$.

Step4: Solve for x

Multiply both sides by - 6: $x=\frac{5}{6}\times(-6)=-5$

Answer:

$x = - 5$