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

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

Solve for x

$$x=9$$

Steps for Solving Linear Equation

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

$$\frac{3}{2}\times 5+\frac{3}{2}\left(-1\right)x+\frac{3}{5}\left(x-4\right)=-3$$

Express \frac{3}{2}\times 5 as a single fraction.

$$\frac{3\times 5}{2}+\frac{3}{2}\left(-1\right)x+\frac{3}{5}\left(x-4\right)=-3$$

Multiply 3 and 5 to get 15.

$$\frac{15}{2}+\frac{3}{2}\left(-1\right)x+\frac{3}{5}\left(x-4\right)=-3$$

Multiply \frac{3}{2} and -1 to get -\frac{3}{2}.

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

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

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

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

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

Multiply 3 and -4 to get -12.

$$\frac{15}{2}-\frac{3}{2}x+\frac{3}{5}x+\frac{-12}{5}=-3$$

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

$$\frac{15}{2}-\frac{3}{2}x+\frac{3}{5}x-\frac{12}{5}=-3$$

Combine -\frac{3}{2}x and \frac{3}{5}x to get -\frac{9}{10}x.

$$\frac{15}{2}-\frac{9}{10}x-\frac{12}{5}=-3$$

Least common multiple of 2 and 5 is 10. Convert \frac{15}{2} and \frac{12}{5} to fractions with denominator 10.

$$\frac{75}{10}-\frac{9}{10}x-\frac{24}{10}=-3$$

Since \frac{75}{10} and \frac{24}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{75-24}{10}-\frac{9}{10}x=-3$$

Subtract 24 from 75 to get 51.

$$\frac{51}{10}-\frac{9}{10}x=-3$$

Subtract \frac{51}{10} from both sides.

$$-\frac{9}{10}x=-3-\frac{51}{10}$$

Convert -3 to fraction -\frac{30}{10}.

$$-\frac{9}{10}x=-\frac{30}{10}-\frac{51}{10}$$

Since -\frac{30}{10} and \frac{51}{10} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{9}{10}x=\frac{-30-51}{10}$$

Subtract 51 from -30 to get -81.

$$-\frac{9}{10}x=-\frac{81}{10}$$

Multiply both sides by -\frac{10}{9}, the reciprocal of -\frac{9}{10}.

$$x=-\frac{81}{10}\left(-\frac{10}{9}\right)$$

Multiply -\frac{81}{10} times -\frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-81\left(-10\right)}{10\times 9}$$

Do the multiplications in the fraction \frac{-81\left(-10\right)}{10\times 9}.

$$x=\frac{810}{90}$$

Divide 810 by 90 to get 9.

$$x=9$$