Solve 1/8x-2=-5(6/5x-1/10)+3/2x+frac{7}{8}x

$$\frac { 1 } { 8 } x - 2 = - 5 ( \frac { 6 } { 5 } x - \frac { 1 } { 10 } ) + \frac { 3 } { 2 } x + \frac { 7 } { 8 } x$$

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply -5 by \frac{6}{5}x-\frac{1}{10}.

$$\frac{1}{8}x-2=-5\times \frac{6}{5}x-5\left(-\frac{1}{10}\right)+\frac{3}{2}x+\frac{7}{8}x$$

Multiply -5 times \frac{6}{5}.

$$\frac{1}{8}x-2=-6x-5\left(-\frac{1}{10}\right)+\frac{3}{2}x+\frac{7}{8}x$$

Express -5\left(-\frac{1}{10}\right) as a single fraction.

$$\frac{1}{8}x-2=-6x+\frac{-5\left(-1\right)}{10}+\frac{3}{2}x+\frac{7}{8}x$$

Multiply -5 and -1 to get 5.

$$\frac{1}{8}x-2=-6x+\frac{5}{10}+\frac{3}{2}x+\frac{7}{8}x$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{8}x-2=-6x+\frac{1}{2}+\frac{3}{2}x+\frac{7}{8}x$$

Combine -6x and \frac{3}{2}x to get -\frac{9}{2}x.

$$\frac{1}{8}x-2=-\frac{9}{2}x+\frac{1}{2}+\frac{7}{8}x$$

Combine -\frac{9}{2}x and \frac{7}{8}x to get -\frac{29}{8}x.

$$\frac{1}{8}x-2=-\frac{29}{8}x+\frac{1}{2}$$

Add \frac{29}{8}x to both sides.

$$\frac{1}{8}x-2+\frac{29}{8}x=\frac{1}{2}$$

Combine \frac{1}{8}x and \frac{29}{8}x to get \frac{15}{4}x.

$$\frac{15}{4}x-2=\frac{1}{2}$$

Add 2 to both sides.

$$\frac{15}{4}x=\frac{1}{2}+2$$

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

$$\frac{15}{4}x=\frac{1}{2}+\frac{4}{2}$$

Since \frac{1}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

$$\frac{15}{4}x=\frac{1+4}{2}$$

Add 1 and 4 to get 5.

$$\frac{15}{4}x=\frac{5}{2}$$

Multiply both sides by \frac{4}{15}, the reciprocal of \frac{15}{4}.

$$x=\frac{5}{2}\times \frac{4}{15}$$

Multiply \frac{5}{2} times \frac{4}{15} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{5\times 4}{2\times 15}$$

Do the multiplications in the fraction \frac{5\times 4}{2\times 15}.

$$x=\frac{20}{30}$$

Reduce the fraction \frac{20}{30} to lowest terms by extracting and canceling out 10.

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