Solve 3/8+x-5/12*(2x-5)=-2-1/8x+7/3

$$\frac{ 3 }{ 8 } +x- \frac{ 5 }{ 12 } \times (2x-5)=-2- \frac{ 1 }{ 8 } x+ \frac{ 7 }{ 3 }$$

Solve for x

$$x = -\frac{51}{7} = -7\frac{2}{7} \approx -7.285714286$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{5}{12} by 2x-5.

$$\frac{3}{8}+x-\frac{5}{12}\times 2x-\frac{5}{12}\left(-5\right)=-2-\frac{1}{8}x+\frac{7}{3}$$

Express -\frac{5}{12}\times 2 as a single fraction.

$$\frac{3}{8}+x+\frac{-5\times 2}{12}x-\frac{5}{12}\left(-5\right)=-2-\frac{1}{8}x+\frac{7}{3}$$

Multiply -5 and 2 to get -10.

$$\frac{3}{8}+x+\frac{-10}{12}x-\frac{5}{12}\left(-5\right)=-2-\frac{1}{8}x+\frac{7}{3}$$

Reduce the fraction \frac{-10}{12} to lowest terms by extracting and canceling out 2.

$$\frac{3}{8}+x-\frac{5}{6}x-\frac{5}{12}\left(-5\right)=-2-\frac{1}{8}x+\frac{7}{3}$$

Express -\frac{5}{12}\left(-5\right) as a single fraction.

$$\frac{3}{8}+x-\frac{5}{6}x+\frac{-5\left(-5\right)}{12}=-2-\frac{1}{8}x+\frac{7}{3}$$

Multiply -5 and -5 to get 25.

$$\frac{3}{8}+x-\frac{5}{6}x+\frac{25}{12}=-2-\frac{1}{8}x+\frac{7}{3}$$

Combine x and -\frac{5}{6}x to get \frac{1}{6}x.

$$\frac{3}{8}+\frac{1}{6}x+\frac{25}{12}=-2-\frac{1}{8}x+\frac{7}{3}$$

Least common multiple of 8 and 12 is 24. Convert \frac{3}{8} and \frac{25}{12} to fractions with denominator 24.

$$\frac{9}{24}+\frac{1}{6}x+\frac{50}{24}=-2-\frac{1}{8}x+\frac{7}{3}$$

Since \frac{9}{24} and \frac{50}{24} have the same denominator, add them by adding their numerators.

$$\frac{9+50}{24}+\frac{1}{6}x=-2-\frac{1}{8}x+\frac{7}{3}$$

Add 9 and 50 to get 59.

$$\frac{59}{24}+\frac{1}{6}x=-2-\frac{1}{8}x+\frac{7}{3}$$

Convert -2 to fraction -\frac{6}{3}.

$$\frac{59}{24}+\frac{1}{6}x=-\frac{6}{3}-\frac{1}{8}x+\frac{7}{3}$$

Since -\frac{6}{3} and \frac{7}{3} have the same denominator, add them by adding their numerators.

$$\frac{59}{24}+\frac{1}{6}x=\frac{-6+7}{3}-\frac{1}{8}x$$

Add -6 and 7 to get 1.

$$\frac{59}{24}+\frac{1}{6}x=\frac{1}{3}-\frac{1}{8}x$$

Add \frac{1}{8}x to both sides.

$$\frac{59}{24}+\frac{1}{6}x+\frac{1}{8}x=\frac{1}{3}$$

Combine \frac{1}{6}x and \frac{1}{8}x to get \frac{7}{24}x.

$$\frac{59}{24}+\frac{7}{24}x=\frac{1}{3}$$

Subtract \frac{59}{24} from both sides.

$$\frac{7}{24}x=\frac{1}{3}-\frac{59}{24}$$

Least common multiple of 3 and 24 is 24. Convert \frac{1}{3} and \frac{59}{24} to fractions with denominator 24.

$$\frac{7}{24}x=\frac{8}{24}-\frac{59}{24}$$

Since \frac{8}{24} and \frac{59}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{24}x=\frac{8-59}{24}$$

Subtract 59 from 8 to get -51.

$$\frac{7}{24}x=\frac{-51}{24}$$

Reduce the fraction \frac{-51}{24} to lowest terms by extracting and canceling out 3.

$$\frac{7}{24}x=-\frac{17}{8}$$

Multiply both sides by \frac{24}{7}, the reciprocal of \frac{7}{24}.

$$x=-\frac{17}{8}\times \frac{24}{7}$$

Multiply -\frac{17}{8} times \frac{24}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-17\times 24}{8\times 7}$$

Do the multiplications in the fraction \frac{-17\times 24}{8\times 7}.

$$x=\frac{-408}{56}$$

Reduce the fraction \frac{-408}{56} to lowest terms by extracting and canceling out 8.

$$x=-\frac{51}{7}$$