Solve -1/2(3/5x-2/3)=9/8

$$\frac { - 1 } { 2 } ( \frac { 3 } { 5 } x - \frac { 2 } { 3 } ) = \frac { 9 } { 8 }$$

Solve for x

$$x = -\frac{95}{36} = -2\frac{23}{36} \approx -2.638888889$$

Steps for Solving Linear Equation

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$-\frac{1}{2}\left(\frac{3}{5}x-\frac{2}{3}\right)=\frac{9}{8}$$

Use the distributive property to multiply -\frac{1}{2} by \frac{3}{5}x-\frac{2}{3}.

$$-\frac{1}{2}\times \frac{3}{5}x-\frac{1}{2}\left(-\frac{2}{3}\right)=\frac{9}{8}$$

Multiply -\frac{1}{2} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3}{2\times 5}x-\frac{1}{2}\left(-\frac{2}{3}\right)=\frac{9}{8}$$

Do the multiplications in the fraction \frac{-3}{2\times 5}.

$$\frac{-3}{10}x-\frac{1}{2}\left(-\frac{2}{3}\right)=\frac{9}{8}$$

Fraction \frac{-3}{10} can be rewritten as -\frac{3}{10} by extracting the negative sign.

$$-\frac{3}{10}x-\frac{1}{2}\left(-\frac{2}{3}\right)=\frac{9}{8}$$

Multiply -\frac{1}{2} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{3}{10}x+\frac{-\left(-2\right)}{2\times 3}=\frac{9}{8}$$

Do the multiplications in the fraction \frac{-\left(-2\right)}{2\times 3}.

$$-\frac{3}{10}x+\frac{2}{6}=\frac{9}{8}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{10}x+\frac{1}{3}=\frac{9}{8}$$

Subtract \frac{1}{3} from both sides.

$$-\frac{3}{10}x=\frac{9}{8}-\frac{1}{3}$$

Least common multiple of 8 and 3 is 24. Convert \frac{9}{8} and \frac{1}{3} to fractions with denominator 24.

$$-\frac{3}{10}x=\frac{27}{24}-\frac{8}{24}$$

Since \frac{27}{24} and \frac{8}{24} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{10}x=\frac{27-8}{24}$$

Subtract 8 from 27 to get 19.

$$-\frac{3}{10}x=\frac{19}{24}$$

Multiply both sides by -\frac{10}{3}, the reciprocal of -\frac{3}{10}.

$$x=\frac{19}{24}\left(-\frac{10}{3}\right)$$

Multiply \frac{19}{24} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{19\left(-10\right)}{24\times 3}$$

Do the multiplications in the fraction \frac{19\left(-10\right)}{24\times 3}.

$$x=\frac{-190}{72}$$

Reduce the fraction \frac{-190}{72} to lowest terms by extracting and canceling out 2.

$$x=-\frac{95}{36}$$