Solve 1-1/2x=3-1/3(x-1)

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

Solve for x

$$x=-14$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{3} by x-1.

$$1-\frac{1}{2}x=3-\frac{1}{3}x-\frac{1}{3}\left(-1\right)$$

Multiply -\frac{1}{3} and -1 to get \frac{1}{3}.

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

Convert 3 to fraction \frac{9}{3}.

$$1-\frac{1}{2}x=\frac{9}{3}-\frac{1}{3}x+\frac{1}{3}$$

Since \frac{9}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$1-\frac{1}{2}x=\frac{9+1}{3}-\frac{1}{3}x$$

Add 9 and 1 to get 10.

$$1-\frac{1}{2}x=\frac{10}{3}-\frac{1}{3}x$$

Add \frac{1}{3}x to both sides.

$$1-\frac{1}{2}x+\frac{1}{3}x=\frac{10}{3}$$

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

$$1-\frac{1}{6}x=\frac{10}{3}$$

Subtract 1 from both sides.

$$-\frac{1}{6}x=\frac{10}{3}-1$$

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

$$-\frac{1}{6}x=\frac{10}{3}-\frac{3}{3}$$

Since \frac{10}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{6}x=\frac{10-3}{3}$$

Subtract 3 from 10 to get 7.

$$-\frac{1}{6}x=\frac{7}{3}$$

Multiply both sides by -6, the reciprocal of -\frac{1}{6}.

$$x=\frac{7}{3}\left(-6\right)$$

Express \frac{7}{3}\left(-6\right) as a single fraction.

$$x=\frac{7\left(-6\right)}{3}$$

Multiply 7 and -6 to get -42.

$$x=\frac{-42}{3}$$

Divide -42 by 3 to get -14.

$$x=-14$$