Solve 3/5(x-4)-(x-3)=2(3/4x+7/3)

$$\frac { 3 } { 5 } ( x - 4 ) - ( x - 3 ) = 2 ( \frac { 3 } { 4 } x + \frac { 7 } { 3 } )$$

Solve for x

$$x = -\frac{122}{57} = -2\frac{8}{57} \approx -2.140350877$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{5} by x-4.

$$\frac{3}{5}x+\frac{3}{5}\left(-4\right)-\left(x-3\right)=2\left(\frac{3}{4}x+\frac{7}{3}\right)$$

Express \frac{3}{5}\left(-4\right) as a single fraction.

$$\frac{3}{5}x+\frac{3\left(-4\right)}{5}-\left(x-3\right)=2\left(\frac{3}{4}x+\frac{7}{3}\right)$$

Multiply 3 and -4 to get -12.

$$\frac{3}{5}x+\frac{-12}{5}-\left(x-3\right)=2\left(\frac{3}{4}x+\frac{7}{3}\right)$$

Fraction \frac{-12}{5} can be rewritten as -\frac{12}{5} by extracting the negative sign.

$$\frac{3}{5}x-\frac{12}{5}-\left(x-3\right)=2\left(\frac{3}{4}x+\frac{7}{3}\right)$$

To find the opposite of x-3, find the opposite of each term.

$$\frac{3}{5}x-\frac{12}{5}-x-\left(-3\right)=2\left(\frac{3}{4}x+\frac{7}{3}\right)$$

The opposite of -3 is 3.

$$\frac{3}{5}x-\frac{12}{5}-x+3=2\left(\frac{3}{4}x+\frac{7}{3}\right)$$

Combine \frac{3}{5}x and -x to get -\frac{2}{5}x.

$$-\frac{2}{5}x-\frac{12}{5}+3=2\left(\frac{3}{4}x+\frac{7}{3}\right)$$

Convert 3 to fraction \frac{15}{5}.

$$-\frac{2}{5}x-\frac{12}{5}+\frac{15}{5}=2\left(\frac{3}{4}x+\frac{7}{3}\right)$$

Since -\frac{12}{5} and \frac{15}{5} have the same denominator, add them by adding their numerators.

$$-\frac{2}{5}x+\frac{-12+15}{5}=2\left(\frac{3}{4}x+\frac{7}{3}\right)$$

Add -12 and 15 to get 3.

$$-\frac{2}{5}x+\frac{3}{5}=2\left(\frac{3}{4}x+\frac{7}{3}\right)$$

Use the distributive property to multiply 2 by \frac{3}{4}x+\frac{7}{3}.

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

Express 2\times \frac{3}{4} as a single fraction.

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

Multiply 2 and 3 to get 6.

$$-\frac{2}{5}x+\frac{3}{5}=\frac{6}{4}x+2\times \frac{7}{3}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{5}x+\frac{3}{5}=\frac{3}{2}x+2\times \frac{7}{3}$$

Express 2\times \frac{7}{3} as a single fraction.

$$-\frac{2}{5}x+\frac{3}{5}=\frac{3}{2}x+\frac{2\times 7}{3}$$

Multiply 2 and 7 to get 14.

$$-\frac{2}{5}x+\frac{3}{5}=\frac{3}{2}x+\frac{14}{3}$$

Subtract \frac{3}{2}x from both sides.

$$-\frac{2}{5}x+\frac{3}{5}-\frac{3}{2}x=\frac{14}{3}$$

Combine -\frac{2}{5}x and -\frac{3}{2}x to get -\frac{19}{10}x.

$$-\frac{19}{10}x+\frac{3}{5}=\frac{14}{3}$$

Subtract \frac{3}{5} from both sides.

$$-\frac{19}{10}x=\frac{14}{3}-\frac{3}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{14}{3} and \frac{3}{5} to fractions with denominator 15.

$$-\frac{19}{10}x=\frac{70}{15}-\frac{9}{15}$$

Since \frac{70}{15} and \frac{9}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{19}{10}x=\frac{70-9}{15}$$

Subtract 9 from 70 to get 61.

$$-\frac{19}{10}x=\frac{61}{15}$$

Multiply both sides by -\frac{10}{19}, the reciprocal of -\frac{19}{10}.

$$x=\frac{61}{15}\left(-\frac{10}{19}\right)$$

Multiply \frac{61}{15} times -\frac{10}{19} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{61\left(-10\right)}{15\times 19}$$

Do the multiplications in the fraction \frac{61\left(-10\right)}{15\times 19}.

$$x=\frac{-610}{285}$$

Reduce the fraction \frac{-610}{285} to lowest terms by extracting and canceling out 5.

$$x=-\frac{122}{57}$$