Solve 1/3x+2-5/6x+3=x-2

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

Solve for x

$$x = \frac{14}{3} = 4\frac{2}{3} \approx 4.666666667$$

Steps for Solving Linear Equation

Combine \frac{1}{3}x and -\frac{5}{6}x to get -\frac{1}{2}x.

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

Add 2 and 3 to get 5.

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

Subtract x from both sides.

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

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

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

Subtract 5 from both sides.

$$-\frac{3}{2}x=-2-5$$

Subtract 5 from -2 to get -7.

$$-\frac{3}{2}x=-7$$

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}.

$$x=-7\left(-\frac{2}{3}\right)$$

Express -7\left(-\frac{2}{3}\right) as a single fraction.

$$x=\frac{-7\left(-2\right)}{3}$$

Multiply -7 and -2 to get 14.

$$x=\frac{14}{3}$$