Solve -3/4(4c-4)+7/8c=31/16

$$- \frac { 3 } { 4 } ( 4 c - 4 ) + \frac { 7 } { 8 } c = \frac { 31 } { 16 }$$

Solve for c

$$c=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{3}{4} by 4c-4.

$$-\frac{3}{4}\times 4c-\frac{3}{4}\left(-4\right)+\frac{7}{8}c=\frac{31}{16}$$

Cancel out 4 and 4.

$$-3c-\frac{3}{4}\left(-4\right)+\frac{7}{8}c=\frac{31}{16}$$

Express -\frac{3}{4}\left(-4\right) as a single fraction.

$$-3c+\frac{-3\left(-4\right)}{4}+\frac{7}{8}c=\frac{31}{16}$$

Multiply -3 and -4 to get 12.

$$-3c+\frac{12}{4}+\frac{7}{8}c=\frac{31}{16}$$

Divide 12 by 4 to get 3.

$$-3c+3+\frac{7}{8}c=\frac{31}{16}$$

Combine -3c and \frac{7}{8}c to get -\frac{17}{8}c.

$$-\frac{17}{8}c+3=\frac{31}{16}$$

Subtract 3 from both sides.

$$-\frac{17}{8}c=\frac{31}{16}-3$$

Convert 3 to fraction \frac{48}{16}.

$$-\frac{17}{8}c=\frac{31}{16}-\frac{48}{16}$$

Since \frac{31}{16} and \frac{48}{16} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{17}{8}c=\frac{31-48}{16}$$

Subtract 48 from 31 to get -17.

$$-\frac{17}{8}c=-\frac{17}{16}$$

Multiply both sides by -\frac{8}{17}, the reciprocal of -\frac{17}{8}.

$$c=-\frac{17}{16}\left(-\frac{8}{17}\right)$$

Multiply -\frac{17}{16} times -\frac{8}{17} by multiplying numerator times numerator and denominator times denominator.

$$c=\frac{-17\left(-8\right)}{16\times 17}$$

Do the multiplications in the fraction \frac{-17\left(-8\right)}{16\times 17}.

$$c=\frac{136}{272}$$

Reduce the fraction \frac{136}{272} to lowest terms by extracting and canceling out 136.

$$c=\frac{1}{2}$$