Solve 0.7*(-5/6)+x*(2/3-1/2)=-5/12

$$0.7 \times (- \frac{ 5 }{ 6 } )+x \times ( \frac{ 2 }{ 3 } - \frac{ 1 }{ 2 } )=- \frac{ 5 }{ 12 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Convert decimal number 0.7 to fraction \frac{7}{10}.

$$\frac{7}{10}\left(-\frac{5}{6}\right)+x\left(\frac{2}{3}-\frac{1}{2}\right)=-\frac{5}{12}$$

Multiply \frac{7}{10} times -\frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(-5\right)}{10\times 6}+x\left(\frac{2}{3}-\frac{1}{2}\right)=-\frac{5}{12}$$

Do the multiplications in the fraction \frac{7\left(-5\right)}{10\times 6}.

$$\frac{-35}{60}+x\left(\frac{2}{3}-\frac{1}{2}\right)=-\frac{5}{12}$$

Reduce the fraction \frac{-35}{60} to lowest terms by extracting and canceling out 5.

$$-\frac{7}{12}+x\left(\frac{2}{3}-\frac{1}{2}\right)=-\frac{5}{12}$$

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

$$-\frac{7}{12}+x\left(\frac{4}{6}-\frac{3}{6}\right)=-\frac{5}{12}$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{7}{12}+x\times \frac{4-3}{6}=-\frac{5}{12}$$

Subtract 3 from 4 to get 1.

$$-\frac{7}{12}+x\times \frac{1}{6}=-\frac{5}{12}$$

Add \frac{7}{12} to both sides.

$$x\times \frac{1}{6}=-\frac{5}{12}+\frac{7}{12}$$

Since -\frac{5}{12} and \frac{7}{12} have the same denominator, add them by adding their numerators.

$$x\times \frac{1}{6}=\frac{-5+7}{12}$$

Add -5 and 7 to get 2.

$$x\times \frac{1}{6}=\frac{2}{12}$$

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

$$x\times \frac{1}{6}=\frac{1}{6}$$

Multiply both sides by 6, the reciprocal of \frac{1}{6}.

$$x=\frac{1}{6}\times 6$$

Cancel out 6 and 6.

$$x=1$$