Solve 1/3x-7/5=-x+7/3

$$\frac{ 1 }{ 3 } x- \frac{ 7 }{ 5 } =-x+ \frac{ 7 }{ 3 }$$

Solve for x

$$x = \frac{14}{5} = 2\frac{4}{5} = 2.8$$

Steps for Solving Linear Equation

Add x to both sides.

$$\frac{1}{3}x-\frac{7}{5}+x=\frac{7}{3}$$

Combine \frac{1}{3}x and x to get \frac{4}{3}x.

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

Add \frac{7}{5} to both sides.

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

Least common multiple of 3 and 5 is 15. Convert \frac{7}{3} and \frac{7}{5} to fractions with denominator 15.

$$\frac{4}{3}x=\frac{35}{15}+\frac{21}{15}$$

Since \frac{35}{15} and \frac{21}{15} have the same denominator, add them by adding their numerators.

$$\frac{4}{3}x=\frac{35+21}{15}$$

Add 35 and 21 to get 56.

$$\frac{4}{3}x=\frac{56}{15}$$

Multiply both sides by \frac{3}{4}, the reciprocal of \frac{4}{3}.

$$x=\frac{56}{15}\times \frac{3}{4}$$

Multiply \frac{56}{15} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{56\times 3}{15\times 4}$$

Do the multiplications in the fraction \frac{56\times 3}{15\times 4}.

$$x=\frac{168}{60}$$

Reduce the fraction \frac{168}{60} to lowest terms by extracting and canceling out 12.

$$x=\frac{14}{5}$$