Solve 2/3x-1/4=1/3-2

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

Solve for x

$$x = -\frac{17}{8} = -2\frac{1}{8} = -2.125$$

Steps for Solving Linear Equation

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

$$\frac{2}{3}x-\frac{1}{4}=\frac{1}{3}-\frac{6}{3}$$

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

$$\frac{2}{3}x-\frac{1}{4}=\frac{1-6}{3}$$

Subtract 6 from 1 to get -5.

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

Add \frac{1}{4} to both sides.

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

Least common multiple of 3 and 4 is 12. Convert -\frac{5}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{2}{3}x=-\frac{20}{12}+\frac{3}{12}$$

Since -\frac{20}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}x=\frac{-20+3}{12}$$

Add -20 and 3 to get -17.

$$\frac{2}{3}x=-\frac{17}{12}$$

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

$$x=-\frac{17}{12}\times \frac{3}{2}$$

Multiply -\frac{17}{12} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-17\times 3}{12\times 2}$$

Do the multiplications in the fraction \frac{-17\times 3}{12\times 2}.

$$x=\frac{-51}{24}$$

Reduce the fraction \frac{-51}{24} to lowest terms by extracting and canceling out 3.

$$x=-\frac{17}{8}$$