Solve 1/6x+1=1/2x-2/3

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

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Subtract \frac{1}{2}x from both sides.

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

Combine \frac{1}{6}x and -\frac{1}{2}x to get -\frac{1}{3}x.

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

Subtract 1 from both sides.

$$-\frac{1}{3}x=-\frac{2}{3}-1$$

Convert 1 to fraction \frac{3}{3}.

$$-\frac{1}{3}x=-\frac{2}{3}-\frac{3}{3}$$

Since -\frac{2}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{3}x=\frac{-2-3}{3}$$

Subtract 3 from -2 to get -5.

$$-\frac{1}{3}x=-\frac{5}{3}$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}.

$$x=-\frac{5}{3}\left(-3\right)$$

Express -\frac{5}{3}\left(-3\right) as a single fraction.

$$x=\frac{-5\left(-3\right)}{3}$$

Multiply -5 and -3 to get 15.

$$x=\frac{15}{3}$$

Divide 15 by 3 to get 5.

$$x=5$$