Solve 2/3-5/8x+7/2=168/4

$$\frac { 2 } { 3 } - \frac { 5 } { 8 } x + \frac { 7 } { 2 } = \frac { 168 } { 4 }$$

Solve for x

$$x = -\frac{908}{15} = -60\frac{8}{15} \approx -60.533333333$$

Steps for Solving Linear Equation

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

$$\frac{4}{6}-\frac{5}{8}x+\frac{21}{6}=\frac{168}{4}$$

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

$$\frac{4+21}{6}-\frac{5}{8}x=\frac{168}{4}$$

Add 4 and 21 to get 25.

$$\frac{25}{6}-\frac{5}{8}x=\frac{168}{4}$$

Divide 168 by 4 to get 42.

$$\frac{25}{6}-\frac{5}{8}x=42$$

Subtract \frac{25}{6} from both sides.

$$-\frac{5}{8}x=42-\frac{25}{6}$$

Convert 42 to fraction \frac{252}{6}.

$$-\frac{5}{8}x=\frac{252}{6}-\frac{25}{6}$$

Since \frac{252}{6} and \frac{25}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{8}x=\frac{252-25}{6}$$

Subtract 25 from 252 to get 227.

$$-\frac{5}{8}x=\frac{227}{6}$$

Multiply both sides by -\frac{8}{5}, the reciprocal of -\frac{5}{8}.

$$x=\frac{227}{6}\left(-\frac{8}{5}\right)$$

Multiply \frac{227}{6} times -\frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{227\left(-8\right)}{6\times 5}$$

Do the multiplications in the fraction \frac{227\left(-8\right)}{6\times 5}.

$$x=\frac{-1816}{30}$$

Reduce the fraction \frac{-1816}{30} to lowest terms by extracting and canceling out 2.

$$x=-\frac{908}{15}$$