Solve 6(120-160/150x)=320-x

$$6 ( 120 - \frac { 160 } { 150 } x ) = 320 - x$$

Solve for x

$$x = \frac{2000}{27} = 74\frac{2}{27} \approx 74.074074074$$

Steps for Solving Linear Equation

Reduce the fraction \frac{160}{150} to lowest terms by extracting and canceling out 10.

$$6\left(120-\frac{16}{15}x\right)=320-x$$

Use the distributive property to multiply 6 by 120-\frac{16}{15}x.

$$720+6\left(-\frac{16}{15}\right)x=320-x$$

Express 6\left(-\frac{16}{15}\right) as a single fraction.

$$720+\frac{6\left(-16\right)}{15}x=320-x$$

Multiply 6 and -16 to get -96.

$$720+\frac{-96}{15}x=320-x$$

Reduce the fraction \frac{-96}{15} to lowest terms by extracting and canceling out 3.

$$720-\frac{32}{5}x=320-x$$

Add x to both sides.

$$720-\frac{32}{5}x+x=320$$

Combine -\frac{32}{5}x and x to get -\frac{27}{5}x.

$$720-\frac{27}{5}x=320$$

Subtract 720 from both sides.

$$-\frac{27}{5}x=320-720$$

Subtract 720 from 320 to get -400.

$$-\frac{27}{5}x=-400$$

Multiply both sides by -\frac{5}{27}, the reciprocal of -\frac{27}{5}.

$$x=-400\left(-\frac{5}{27}\right)$$

Express -400\left(-\frac{5}{27}\right) as a single fraction.

$$x=\frac{-400\left(-5\right)}{27}$$

Multiply -400 and -5 to get 2000.

$$x=\frac{2000}{27}$$