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 =…

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

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

Answer

Explanation:

Step1: Move x - terms to one side

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

Step2: Combine x - terms

Find a common denominator for the x - terms. The common denominator of 6 and 3 is 6. So $\frac{5}{6}x-\frac{2}{3}x=\frac{5}{6}x-\frac{4}{6}x=\frac{1}{6}x$. The equation becomes $-\frac{1}{2}=\frac{1}{3}+\frac{1}{6}x$.

Step3: Move the constant term to the left - hand side

Subtract $\frac{1}{3}$ from both sides. The common denominator of 2 and 3 is 6. So $-\frac{1}{2}-\frac{1}{3}=-\frac{3}{6}-\frac{2}{6}=-\frac{5}{6}$. The equation is $-\frac{5}{6}=\frac{1}{6}x$.

Step4: Solve for x

Multiply both sides by 6 to get $x=-5$.

Answer:

$x = - 5$