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

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

Solve for x

$$x = -\frac{114}{7} = -16\frac{2}{7} \approx -16.285714286$$

Steps for Solving Linear Equation

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

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

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

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

Multiply -5 and 2 to get -10.

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

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

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

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

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

Multiply -5 and -5 to get 25.

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

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

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

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

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

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

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

Add 9 and 50 to get 59.

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

Use the distributive property to multiply -\frac{1}{8} by x+\frac{7}{3}.

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

Multiply -\frac{1}{8} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Fraction \frac{-7}{24} can be rewritten as -\frac{7}{24} by extracting the negative sign.

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

Convert -2 to fraction -\frac{48}{24}.

$$\frac{59}{24}+\frac{1}{6}x=-\frac{48}{24}-\frac{1}{8}x-\frac{7}{24}$$

Since -\frac{48}{24} and \frac{7}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{59}{24}+\frac{1}{6}x=\frac{-48-7}{24}-\frac{1}{8}x$$

Subtract 7 from -48 to get -55.

$$\frac{59}{24}+\frac{1}{6}x=-\frac{55}{24}-\frac{1}{8}x$$

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

$$\frac{59}{24}+\frac{1}{6}x+\frac{1}{8}x=-\frac{55}{24}$$

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

$$\frac{59}{24}+\frac{7}{24}x=-\frac{55}{24}$$

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

$$\frac{7}{24}x=-\frac{55}{24}-\frac{59}{24}$$

Since -\frac{55}{24} and \frac{59}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{24}x=\frac{-55-59}{24}$$

Subtract 59 from -55 to get -114.

$$\frac{7}{24}x=\frac{-114}{24}$$

Reduce the fraction \frac{-114}{24} to lowest terms by extracting and canceling out 6.

$$\frac{7}{24}x=-\frac{19}{4}$$

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

$$x=-\frac{19}{4}\times \frac{24}{7}$$

Multiply -\frac{19}{4} times \frac{24}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-19\times 24}{4\times 7}$$

Do the multiplications in the fraction \frac{-19\times 24}{4\times 7}.

$$x=\frac{-456}{28}$$

Reduce the fraction \frac{-456}{28} to lowest terms by extracting and canceling out 4.

$$x=-\frac{114}{7}$$