Solve -5x-3/2=1/4x-2/3

$$- 5 x - 3 / 2 = 1 / 4 x - 2 / 3$$

Solve for x

$$x=-\frac{10}{63}\approx -0.158730159$$

Steps for Solving Linear Equation

Subtract \frac{1}{4}x from both sides.

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

Combine -5x and -\frac{1}{4}x to get -\frac{21}{4}x.

$$-\frac{21}{4}x-\frac{3}{2}=-\frac{2}{3}$$

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

$$-\frac{21}{4}x=-\frac{2}{3}+\frac{3}{2}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{2}{3} and \frac{3}{2} to fractions with denominator 6.

$$-\frac{21}{4}x=-\frac{4}{6}+\frac{9}{6}$$

Since -\frac{4}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$-\frac{21}{4}x=\frac{-4+9}{6}$$

Add -4 and 9 to get 5.

$$-\frac{21}{4}x=\frac{5}{6}$$

Multiply both sides by -\frac{4}{21}, the reciprocal of -\frac{21}{4}.

$$x=\frac{5}{6}\left(-\frac{4}{21}\right)$$

Multiply \frac{5}{6} times -\frac{4}{21} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{5\left(-4\right)}{6\times 21}$$

Do the multiplications in the fraction \frac{5\left(-4\right)}{6\times 21}.

$$x=\frac{-20}{126}$$

Reduce the fraction \frac{-20}{126} to lowest terms by extracting and canceling out 2.

$$x=-\frac{10}{63}$$