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

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

Solve for x

$$x = -\frac{12}{5} = -2\frac{2}{5} = -2.4$$

Steps for Solving Linear Equation

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

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

Cancel out 3 and 3.

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

Combine \frac{5}{3}x and x to get \frac{8}{3}x.

$$\frac{8}{3}x+5-5=2\left(3x+4\right)$$

Subtract 5 from 5 to get 0.

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

Use the distributive property to multiply 2 by 3x+4.

$$\frac{8}{3}x=6x+8$$

Subtract 6x from both sides.

$$\frac{8}{3}x-6x=8$$

Combine \frac{8}{3}x and -6x to get -\frac{10}{3}x.

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

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

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

Express 8\left(-\frac{3}{10}\right) as a single fraction.

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

Multiply 8 and -3 to get -24.

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

Reduce the fraction \frac{-24}{10} to lowest terms by extracting and canceling out 2.

$$x=-\frac{12}{5}$$