Solve 10/4x+9=8/5x+7/10

$$\frac { 10 } { 4 } x + 9 = \frac { 8 } { 5 } x + \frac { 7 } { 10 }$$

Solve for x

$$x = -\frac{83}{9} = -9\frac{2}{9} \approx -9.222222222$$

Steps for Solving Linear Equation

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{2}x+9=\frac{8}{5}x+\frac{7}{10}$$

Subtract \frac{8}{5}x from both sides.

$$\frac{5}{2}x+9-\frac{8}{5}x=\frac{7}{10}$$

Combine \frac{5}{2}x and -\frac{8}{5}x to get \frac{9}{10}x.

$$\frac{9}{10}x+9=\frac{7}{10}$$

Subtract 9 from both sides.

$$\frac{9}{10}x=\frac{7}{10}-9$$

Convert 9 to fraction \frac{90}{10}.

$$\frac{9}{10}x=\frac{7}{10}-\frac{90}{10}$$

Since \frac{7}{10} and \frac{90}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{10}x=\frac{7-90}{10}$$

Subtract 90 from 7 to get -83.

$$\frac{9}{10}x=-\frac{83}{10}$$

Multiply both sides by \frac{10}{9}, the reciprocal of \frac{9}{10}.

$$x=-\frac{83}{10}\times \frac{10}{9}$$

Multiply -\frac{83}{10} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-83\times 10}{10\times 9}$$

Cancel out 10 in both numerator and denominator.

$$x=\frac{-83}{9}$$

Fraction \frac{-83}{9} can be rewritten as -\frac{83}{9} by extracting the negative sign.

$$x=-\frac{83}{9}$$