Solve 40x=40/3x+80left(2/3x-1.5right)

$$40x = \frac{ 40 }{ 3 } x+80 \left( \frac{ 2 }{ 3 } x-1.5 \right)$$

Solve for x

$$x=4.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 80 by \frac{2}{3}x-1.5.

$$40x=\frac{40}{3}x+80\times \frac{2}{3}x-120$$

Express 80\times \frac{2}{3} as a single fraction.

$$40x=\frac{40}{3}x+\frac{80\times 2}{3}x-120$$

Multiply 80 and 2 to get 160.

$$40x=\frac{40}{3}x+\frac{160}{3}x-120$$

Combine \frac{40}{3}x and \frac{160}{3}x to get \frac{200}{3}x.

$$40x=\frac{200}{3}x-120$$

Subtract \frac{200}{3}x from both sides.

$$40x-\frac{200}{3}x=-120$$

Combine 40x and -\frac{200}{3}x to get -\frac{80}{3}x.

$$-\frac{80}{3}x=-120$$

Multiply both sides by -\frac{3}{80}, the reciprocal of -\frac{80}{3}.

$$x=-120\left(-\frac{3}{80}\right)$$

Express -120\left(-\frac{3}{80}\right) as a single fraction.

$$x=\frac{-120\left(-3\right)}{80}$$

Multiply -120 and -3 to get 360.

$$x=\frac{360}{80}$$

Reduce the fraction \frac{360}{80} to lowest terms by extracting and canceling out 40.

$$x=\frac{9}{2}$$