Solve 15-x/2/9=15x+2x/2/15

$$\frac { \frac { 15 - x } { 2 } } { 9 } = \frac { \frac { 15 x + 2 x } { 2 } } { 15 }$$

Solve for x

$$x = \frac{75}{56} = 1\frac{19}{56} \approx 1.339285714$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 45, the least common multiple of 9,15.

$$5\times \frac{15-x}{2}=3\times \frac{15x+2x}{2}$$

Express 5\times \frac{15-x}{2} as a single fraction.

$$\frac{5\left(15-x\right)}{2}=3\times \frac{15x+2x}{2}$$

Combine 15x and 2x to get 17x.

$$\frac{5\left(15-x\right)}{2}=3\times \frac{17x}{2}$$

Express 3\times \frac{17x}{2} as a single fraction.

$$\frac{5\left(15-x\right)}{2}=\frac{3\times 17x}{2}$$

Use the distributive property to multiply 5 by 15-x.

$$\frac{75-5x}{2}=\frac{3\times 17x}{2}$$

Divide each term of 75-5x by 2 to get \frac{75}{2}-\frac{5}{2}x.

$$\frac{75}{2}-\frac{5}{2}x=\frac{3\times 17x}{2}$$

Multiply 3 and 17 to get 51.

$$\frac{75}{2}-\frac{5}{2}x=\frac{51x}{2}$$

Subtract \frac{51x}{2} from both sides.

$$\frac{75}{2}-\frac{5}{2}x-\frac{51x}{2}=0$$

Since \frac{75}{2} and \frac{51x}{2} have the same denominator, add them by adding their numerators.

$$\frac{75+51x}{2}-\frac{5}{2}x=0$$

Multiply both sides of the equation by 2.

$$75+51x-5x=0$$

Reorder the terms.

$$-5x+51x+75=0$$

Combine -5x and 51x to get 46x.

$$46x+75=0$$

Subtract 75 from both sides. Anything subtracted from zero gives its negation.

$$46x=-75$$

Divide both sides by 46.

$$x=\frac{-75}{46}$$

Fraction \frac{-75}{46} can be rewritten as -\frac{75}{46} by extracting the negative sign.

$$x=-\frac{75}{46}$$