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

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

Solve for x

$$x=-\frac{21}{26}\approx -0.807692308$$

Steps for Solving Linear Equation

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

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

Combine \frac{2}{3}x and \frac{3}{2}x to get \frac{13}{6}x.

$$\frac{13}{6}x+2=\frac{1}{4}$$

Subtract 2 from both sides.

$$\frac{13}{6}x=\frac{1}{4}-2$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{13}{6}x=\frac{1}{4}-\frac{8}{4}$$

Since \frac{1}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{6}x=\frac{1-8}{4}$$

Subtract 8 from 1 to get -7.

$$\frac{13}{6}x=-\frac{7}{4}$$

Multiply both sides by \frac{6}{13}, the reciprocal of \frac{13}{6}.

$$x=-\frac{7}{4}\times \frac{6}{13}$$

Multiply -\frac{7}{4} times \frac{6}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-7\times 6}{4\times 13}$$

Do the multiplications in the fraction \frac{-7\times 6}{4\times 13}.

$$x=\frac{-42}{52}$$

Reduce the fraction \frac{-42}{52} to lowest terms by extracting and canceling out 2.

$$x=-\frac{21}{26}$$