Solve 3/8(2x-3)-4/3(x-2)=2/3

$$\frac { 3 } { 8 } ( 2 x - 3 ) - \frac { 4 } { 3 } ( x - 2 ) = \frac { 2 } { 3 }$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{8} by 2x-3.

$$\frac{3}{8}\times 2x+\frac{3}{8}\left(-3\right)-\frac{4}{3}\left(x-2\right)=\frac{2}{3}$$

Express \frac{3}{8}\times 2 as a single fraction.

$$\frac{3\times 2}{8}x+\frac{3}{8}\left(-3\right)-\frac{4}{3}\left(x-2\right)=\frac{2}{3}$$

Multiply 3 and 2 to get 6.

$$\frac{6}{8}x+\frac{3}{8}\left(-3\right)-\frac{4}{3}\left(x-2\right)=\frac{2}{3}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}x+\frac{3}{8}\left(-3\right)-\frac{4}{3}\left(x-2\right)=\frac{2}{3}$$

Express \frac{3}{8}\left(-3\right) as a single fraction.

$$\frac{3}{4}x+\frac{3\left(-3\right)}{8}-\frac{4}{3}\left(x-2\right)=\frac{2}{3}$$

Multiply 3 and -3 to get -9.

$$\frac{3}{4}x+\frac{-9}{8}-\frac{4}{3}\left(x-2\right)=\frac{2}{3}$$

Fraction \frac{-9}{8} can be rewritten as -\frac{9}{8} by extracting the negative sign.

$$\frac{3}{4}x-\frac{9}{8}-\frac{4}{3}\left(x-2\right)=\frac{2}{3}$$

Use the distributive property to multiply -\frac{4}{3} by x-2.

$$\frac{3}{4}x-\frac{9}{8}-\frac{4}{3}x-\frac{4}{3}\left(-2\right)=\frac{2}{3}$$

Express -\frac{4}{3}\left(-2\right) as a single fraction.

$$\frac{3}{4}x-\frac{9}{8}-\frac{4}{3}x+\frac{-4\left(-2\right)}{3}=\frac{2}{3}$$

Multiply -4 and -2 to get 8.

$$\frac{3}{4}x-\frac{9}{8}-\frac{4}{3}x+\frac{8}{3}=\frac{2}{3}$$

Combine \frac{3}{4}x and -\frac{4}{3}x to get -\frac{7}{12}x.

$$-\frac{7}{12}x-\frac{9}{8}+\frac{8}{3}=\frac{2}{3}$$

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

$$-\frac{7}{12}x-\frac{27}{24}+\frac{64}{24}=\frac{2}{3}$$

Since -\frac{27}{24} and \frac{64}{24} have the same denominator, add them by adding their numerators.

$$-\frac{7}{12}x+\frac{-27+64}{24}=\frac{2}{3}$$

Add -27 and 64 to get 37.

$$-\frac{7}{12}x+\frac{37}{24}=\frac{2}{3}$$

Subtract \frac{37}{24} from both sides.

$$-\frac{7}{12}x=\frac{2}{3}-\frac{37}{24}$$

Least common multiple of 3 and 24 is 24. Convert \frac{2}{3} and \frac{37}{24} to fractions with denominator 24.

$$-\frac{7}{12}x=\frac{16}{24}-\frac{37}{24}$$

Since \frac{16}{24} and \frac{37}{24} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{7}{12}x=\frac{16-37}{24}$$

Subtract 37 from 16 to get -21.

$$-\frac{7}{12}x=\frac{-21}{24}$$

Reduce the fraction \frac{-21}{24} to lowest terms by extracting and canceling out 3.

$$-\frac{7}{12}x=-\frac{7}{8}$$

Multiply both sides by -\frac{12}{7}, the reciprocal of -\frac{7}{12}.

$$x=-\frac{7}{8}\left(-\frac{12}{7}\right)$$

Multiply -\frac{7}{8} times -\frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-7\left(-12\right)}{8\times 7}$$

Do the multiplications in the fraction \frac{-7\left(-12\right)}{8\times 7}.

$$x=\frac{84}{56}$$

Reduce the fraction \frac{84}{56} to lowest terms by extracting and canceling out 28.

$$x=\frac{3}{2}$$