Solve -1/2x-1/8=x+5/8

$$\frac { - 1 } { 2 } x - \frac { 1 } { 8 } = x + \frac { 5 } { 8 }$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$-\frac{1}{2}x-\frac{1}{8}=x+\frac{5}{8}$$

Subtract x from both sides.

$$-\frac{1}{2}x-\frac{1}{8}-x=\frac{5}{8}$$

Combine -\frac{1}{2}x and -x to get -\frac{3}{2}x.

$$-\frac{3}{2}x-\frac{1}{8}=\frac{5}{8}$$

Add \frac{1}{8} to both sides.

$$-\frac{3}{2}x=\frac{5}{8}+\frac{1}{8}$$

Since \frac{5}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$-\frac{3}{2}x=\frac{5+1}{8}$$

Add 5 and 1 to get 6.

$$-\frac{3}{2}x=\frac{6}{8}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

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

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

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

Multiply \frac{3}{4} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

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