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

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

Solve for x

$$x=-\frac{1}{13}\approx -0.076923077$$

Steps for Solving Linear Equation

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

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

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

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

Divide -2 by 2 to get -1.

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

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

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

Express \frac{3}{4}\times 3 as a single fraction.

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

Multiply 3 and 3 to get 9.

$$\frac{1}{2}-x=\frac{9}{4}x+\frac{3}{4}$$

Subtract \frac{9}{4}x from both sides.

$$\frac{1}{2}-x-\frac{9}{4}x=\frac{3}{4}$$

Combine -x and -\frac{9}{4}x to get -\frac{13}{4}x.

$$\frac{1}{2}-\frac{13}{4}x=\frac{3}{4}$$

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

$$-\frac{13}{4}x=\frac{3}{4}-\frac{1}{2}$$

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

$$-\frac{13}{4}x=\frac{3}{4}-\frac{2}{4}$$

Since \frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{4}x=\frac{3-2}{4}$$

Subtract 2 from 3 to get 1.

$$-\frac{13}{4}x=\frac{1}{4}$$

Multiply both sides by -\frac{4}{13}, the reciprocal of -\frac{13}{4}.

$$x=\frac{1}{4}\left(-\frac{4}{13}\right)$$

Multiply \frac{1}{4} times -\frac{4}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1\left(-4\right)}{4\times 13}$$

Do the multiplications in the fraction \frac{1\left(-4\right)}{4\times 13}.

$$x=\frac{-4}{52}$$

Reduce the fraction \frac{-4}{52} to lowest terms by extracting and canceling out 4.

$$x=-\frac{1}{13}$$