Solve 5/3x+5/2=-7/6x-6

$$\frac { 5 } { 3 } x + \frac { 5 } { 2 } = - \frac { 7 } { 6 } x - 6$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Add \frac{7}{6}x to both sides.

$$\frac{5}{3}x+\frac{5}{2}+\frac{7}{6}x=-6$$

Combine \frac{5}{3}x and \frac{7}{6}x to get \frac{17}{6}x.

$$\frac{17}{6}x+\frac{5}{2}=-6$$

Subtract \frac{5}{2} from both sides.

$$\frac{17}{6}x=-6-\frac{5}{2}$$

Convert -6 to fraction -\frac{12}{2}.

$$\frac{17}{6}x=-\frac{12}{2}-\frac{5}{2}$$

Since -\frac{12}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{6}x=\frac{-12-5}{2}$$

Subtract 5 from -12 to get -17.

$$\frac{17}{6}x=-\frac{17}{2}$$

Multiply both sides by \frac{6}{17}, the reciprocal of \frac{17}{6}.

$$x=-\frac{17}{2}\times \frac{6}{17}$$

Multiply -\frac{17}{2} times \frac{6}{17} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-17\times 6}{2\times 17}$$

Do the multiplications in the fraction \frac{-17\times 6}{2\times 17}.

$$x=\frac{-102}{34}$$

Divide -102 by 34 to get -3.

$$x=-3$$