Solve 2/3left(x-1right)=-7/12left(x+6right)

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

Solve for x

$$x = -\frac{34}{15} = -2\frac{4}{15} \approx -2.266666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by x-1.

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

Multiply \frac{2}{3} and -1 to get -\frac{2}{3}.

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

Use the distributive property to multiply -\frac{7}{12} by x+6.

$$\frac{2}{3}x-\frac{2}{3}=-\frac{7}{12}x-\frac{7}{12}\times 6$$

Express -\frac{7}{12}\times 6 as a single fraction.

$$\frac{2}{3}x-\frac{2}{3}=-\frac{7}{12}x+\frac{-7\times 6}{12}$$

Multiply -7 and 6 to get -42.

$$\frac{2}{3}x-\frac{2}{3}=-\frac{7}{12}x+\frac{-42}{12}$$

Reduce the fraction \frac{-42}{12} to lowest terms by extracting and canceling out 6.

$$\frac{2}{3}x-\frac{2}{3}=-\frac{7}{12}x-\frac{7}{2}$$

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

$$\frac{2}{3}x-\frac{2}{3}+\frac{7}{12}x=-\frac{7}{2}$$

Combine \frac{2}{3}x and \frac{7}{12}x to get \frac{5}{4}x.

$$\frac{5}{4}x-\frac{2}{3}=-\frac{7}{2}$$

Add \frac{2}{3} to both sides.

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

Least common multiple of 2 and 3 is 6. Convert -\frac{7}{2} and \frac{2}{3} to fractions with denominator 6.

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

Since -\frac{21}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

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

Add -21 and 4 to get -17.

$$\frac{5}{4}x=-\frac{17}{6}$$

Multiply both sides by \frac{4}{5}, the reciprocal of \frac{5}{4}.

$$x=-\frac{17}{6}\times \frac{4}{5}$$

Multiply -\frac{17}{6} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-17\times 4}{6\times 5}$$

Do the multiplications in the fraction \frac{-17\times 4}{6\times 5}.

$$x=\frac{-68}{30}$$

Reduce the fraction \frac{-68}{30} to lowest terms by extracting and canceling out 2.

$$x=-\frac{34}{15}$$