Solve 1/3(1-2x)=4-1/2(3x+4)

$$\frac { 1 } { 3 } ( 1 - 2 x ) = 4 - \frac { 1 } { 2 } ( 3 x + 4 )$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by 1-2x.

$$\frac{1}{3}+\frac{1}{3}\left(-2\right)x=4-\frac{1}{2}\left(3x+4\right)$$

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

$$\frac{1}{3}+\frac{-2}{3}x=4-\frac{1}{2}\left(3x+4\right)$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\frac{1}{3}-\frac{2}{3}x=4-\frac{1}{2}\left(3x+4\right)$$

Use the distributive property to multiply -\frac{1}{2} by 3x+4.

$$\frac{1}{3}-\frac{2}{3}x=4-\frac{1}{2}\times 3x-\frac{1}{2}\times 4$$

Express -\frac{1}{2}\times 3 as a single fraction.

$$\frac{1}{3}-\frac{2}{3}x=4+\frac{-3}{2}x-\frac{1}{2}\times 4$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$\frac{1}{3}-\frac{2}{3}x=4-\frac{3}{2}x-\frac{1}{2}\times 4$$

Express -\frac{1}{2}\times 4 as a single fraction.

$$\frac{1}{3}-\frac{2}{3}x=4-\frac{3}{2}x+\frac{-4}{2}$$

Divide -4 by 2 to get -2.

$$\frac{1}{3}-\frac{2}{3}x=4-\frac{3}{2}x-2$$

Subtract 2 from 4 to get 2.

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

Add \frac{3}{2}x to both sides.

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

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

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

Subtract \frac{1}{3} from both sides.

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

Convert 2 to fraction \frac{6}{3}.

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

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 6 to get 5.

$$\frac{5}{6}x=\frac{5}{3}$$

Multiply both sides by \frac{6}{5}, the reciprocal of \frac{5}{6}.

$$x=\frac{5}{3}\times \frac{6}{5}$$

Multiply \frac{5}{3} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{5\times 6}{3\times 5}$$

Cancel out 5 in both numerator and denominator.

$$x=\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$x=2$$