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

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

Solve for x

$$x=-\frac{44}{85}\approx -0.517647059$$

Steps for Solving Linear Equation

Subtract 4x from both sides.

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

Combine -\frac{5}{3}x and -4x to get -\frac{17}{3}x.

$$-\frac{17}{3}x-\frac{3}{5}=\frac{7}{3}$$

Add \frac{3}{5} to both sides.

$$-\frac{17}{3}x=\frac{7}{3}+\frac{3}{5}$$

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

$$-\frac{17}{3}x=\frac{35}{15}+\frac{9}{15}$$

Since \frac{35}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$-\frac{17}{3}x=\frac{35+9}{15}$$

Add 35 and 9 to get 44.

$$-\frac{17}{3}x=\frac{44}{15}$$

Multiply both sides by -\frac{3}{17}, the reciprocal of -\frac{17}{3}.

$$x=\frac{44}{15}\left(-\frac{3}{17}\right)$$

Multiply \frac{44}{15} times -\frac{3}{17} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{44\left(-3\right)}{15\times 17}$$

Do the multiplications in the fraction \frac{44\left(-3\right)}{15\times 17}.

$$x=\frac{-132}{255}$$

Reduce the fraction \frac{-132}{255} to lowest terms by extracting and canceling out 3.

$$x=-\frac{44}{85}$$