Solve 3x+4/3=5x+6/7

$$3 x + \frac { 4 } { 3 } = 5 x + \frac { 6 } { 7 }$$

Solve for x

$$x=\frac{5}{21}\approx 0.238095238$$

Steps for Solving Linear Equation

Subtract 5x from both sides.

$$3x+\frac{4}{3}-5x=\frac{6}{7}$$

Combine 3x and -5x to get -2x.

$$-2x+\frac{4}{3}=\frac{6}{7}$$

Subtract \frac{4}{3} from both sides.

$$-2x=\frac{6}{7}-\frac{4}{3}$$

Least common multiple of 7 and 3 is 21. Convert \frac{6}{7} and \frac{4}{3} to fractions with denominator 21.

$$-2x=\frac{18}{21}-\frac{28}{21}$$

Since \frac{18}{21} and \frac{28}{21} have the same denominator, subtract them by subtracting their numerators.

$$-2x=\frac{18-28}{21}$$

Subtract 28 from 18 to get -10.

$$-2x=-\frac{10}{21}$$

Divide both sides by -2.

$$x=\frac{-\frac{10}{21}}{-2}$$

Express \frac{-\frac{10}{21}}{-2} as a single fraction.

$$x=\frac{-10}{21\left(-2\right)}$$

Multiply 21 and -2 to get -42.

$$x=\frac{-10}{-42}$$

Reduce the fraction \frac{-10}{-42} to lowest terms by extracting and canceling out -2.

$$x=\frac{5}{21}$$