Solve 6(5/6x+2/3)=-9

$$6 ( \frac { 5 } { 6 } x + \frac { 2 } { 3 } ) = - 9$$

Solve for x

$$x = -\frac{13}{5} = -2\frac{3}{5} = -2.6$$

Steps for Solving Linear Equation

Divide both sides by 6.

$$\frac{5}{6}x+\frac{2}{3}=\frac{-9}{6}$$

Reduce the fraction \frac{-9}{6} to lowest terms by extracting and canceling out 3.

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

Subtract \frac{2}{3} from both sides.

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

Least common multiple of 2 and 3 is 6. Convert -\frac{3}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{5}{6}x=-\frac{9}{6}-\frac{4}{6}$$

Since -\frac{9}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}x=\frac{-9-4}{6}$$

Subtract 4 from -9 to get -13.

$$\frac{5}{6}x=-\frac{13}{6}$$

Multiply both sides by \frac{6}{5}, the reciprocal of \frac{5}{6}.

$$x=-\frac{13}{6}\times \frac{6}{5}$$

Multiply -\frac{13}{6} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-13\times 6}{6\times 5}$$

Cancel out 6 in both numerator and denominator.

$$x=\frac{-13}{5}$$

Fraction \frac{-13}{5} can be rewritten as -\frac{13}{5} by extracting the negative sign.

$$x=-\frac{13}{5}$$