Solve 2/3*(-3/4+5/6*x)=-7/8

$$\frac { 2 } { 3 } \cdot ( - \frac { 3 } { 4 } + \frac { 5 } { 6 } \cdot x ) = - \frac { 7 } { 8 }$$

Solve for x

$$x=-\frac{27}{40}=-0.675$$

Steps for Solving Linear Equation

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$-\frac{3}{4}+\frac{5}{6}x=-\frac{7}{8}\times \frac{3}{2}$$

Multiply -\frac{7}{8} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{3}{4}+\frac{5}{6}x=\frac{-7\times 3}{8\times 2}$$

Do the multiplications in the fraction \frac{-7\times 3}{8\times 2}.

$$-\frac{3}{4}+\frac{5}{6}x=\frac{-21}{16}$$

Fraction \frac{-21}{16} can be rewritten as -\frac{21}{16} by extracting the negative sign.

$$-\frac{3}{4}+\frac{5}{6}x=-\frac{21}{16}$$

Add \frac{3}{4} to both sides.

$$\frac{5}{6}x=-\frac{21}{16}+\frac{3}{4}$$

Least common multiple of 16 and 4 is 16. Convert -\frac{21}{16} and \frac{3}{4} to fractions with denominator 16.

$$\frac{5}{6}x=-\frac{21}{16}+\frac{12}{16}$$

Since -\frac{21}{16} and \frac{12}{16} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}x=\frac{-21+12}{16}$$

Add -21 and 12 to get -9.

$$\frac{5}{6}x=-\frac{9}{16}$$

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

$$x=-\frac{9}{16}\times \frac{6}{5}$$

Multiply -\frac{9}{16} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-9\times 6}{16\times 5}$$

Do the multiplications in the fraction \frac{-9\times 6}{16\times 5}.

$$x=\frac{-54}{80}$$

Reduce the fraction \frac{-54}{80} to lowest terms by extracting and canceling out 2.

$$x=-\frac{27}{40}$$