Solve x+7/15/3=x-7/15/2

$$\frac{ x+ \frac{ 7 }{ 15 } }{ 3 } = \frac{ x- \frac{ 7 }{ 15 } }{ 2 }$$

Solve for x

$$x = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2\left(x+\frac{7}{15}\right)=3\left(x-\frac{7}{15}\right)$$

Use the distributive property to multiply 2 by x+\frac{7}{15}.

$$2x+2\times \frac{7}{15}=3\left(x-\frac{7}{15}\right)$$

Express 2\times \frac{7}{15} as a single fraction.

$$2x+\frac{2\times 7}{15}=3\left(x-\frac{7}{15}\right)$$

Multiply 2 and 7 to get 14.

$$2x+\frac{14}{15}=3\left(x-\frac{7}{15}\right)$$

Use the distributive property to multiply 3 by x-\frac{7}{15}.

$$2x+\frac{14}{15}=3x+3\left(-\frac{7}{15}\right)$$

Express 3\left(-\frac{7}{15}\right) as a single fraction.

$$2x+\frac{14}{15}=3x+\frac{3\left(-7\right)}{15}$$

Multiply 3 and -7 to get -21.

$$2x+\frac{14}{15}=3x+\frac{-21}{15}$$

Reduce the fraction \frac{-21}{15} to lowest terms by extracting and canceling out 3.

$$2x+\frac{14}{15}=3x-\frac{7}{5}$$

Subtract 3x from both sides.

$$2x+\frac{14}{15}-3x=-\frac{7}{5}$$

Combine 2x and -3x to get -x.

$$-x+\frac{14}{15}=-\frac{7}{5}$$

Subtract \frac{14}{15} from both sides.

$$-x=-\frac{7}{5}-\frac{14}{15}$$

Least common multiple of 5 and 15 is 15. Convert -\frac{7}{5} and \frac{14}{15} to fractions with denominator 15.

$$-x=-\frac{21}{15}-\frac{14}{15}$$

Since -\frac{21}{15} and \frac{14}{15} have the same denominator, subtract them by subtracting their numerators.

$$-x=\frac{-21-14}{15}$$

Subtract 14 from -21 to get -35.

$$-x=\frac{-35}{15}$$

Reduce the fraction \frac{-35}{15} to lowest terms by extracting and canceling out 5.

$$-x=-\frac{7}{3}$$

Multiply both sides by -1.

$$x=\frac{7}{3}$$