Solve 4/3x+1/2-5/3x=1/4-1-frac{3}{4}x

$$\frac { 4 } { 3 } x + \frac { 1 } { 2 } - \frac { 5 } { 3 } x = \frac { 1 } { 4 } - 1 - \frac { 3 } { 4 } x$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Combine \frac{4}{3}x and -\frac{5}{3}x to get -\frac{1}{3}x.

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

Convert 1 to fraction \frac{4}{4}.

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

Since \frac{1}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 1 to get -3.

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

Add \frac{3}{4}x to both sides.

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

Combine -\frac{1}{3}x and \frac{3}{4}x to get \frac{5}{12}x.

$$\frac{5}{12}x+\frac{1}{2}=-\frac{3}{4}$$

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

$$\frac{5}{12}x=-\frac{3}{4}-\frac{1}{2}$$

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

$$\frac{5}{12}x=-\frac{3}{4}-\frac{2}{4}$$

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

$$\frac{5}{12}x=\frac{-3-2}{4}$$

Subtract 2 from -3 to get -5.

$$\frac{5}{12}x=-\frac{5}{4}$$

Multiply both sides by \frac{12}{5}, the reciprocal of \frac{5}{12}.

$$x=-\frac{5}{4}\times \frac{12}{5}$$

Multiply -\frac{5}{4} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-5\times 12}{4\times 5}$$

Do the multiplications in the fraction \frac{-5\times 12}{4\times 5}.

$$x=\frac{-60}{20}$$

Divide -60 by 20 to get -3.

$$x=-3$$