Solve 360+1.6x<400+2(x-8)*75%

$$360 + 1.6 x < 400 + 2 ( x - 8 ) \cdot 75 \%$$

Solve for x

$$x<280$$

Solution Steps

Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$360+1.6x<400+2\left(x-8\right)\times \frac{3}{4}$$

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

$$360+1.6x<400+\frac{2\times 3}{4}\left(x-8\right)$$

Multiply 2 and 3 to get 6.

$$360+1.6x<400+\frac{6}{4}\left(x-8\right)$$

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

$$360+1.6x<400+\frac{3}{2}\left(x-8\right)$$

Use the distributive property to multiply \frac{3}{2} by x-8.

$$360+1.6x<400+\frac{3}{2}x+\frac{3}{2}\left(-8\right)$$

Express \frac{3}{2}\left(-8\right) as a single fraction.

$$360+1.6x<400+\frac{3}{2}x+\frac{3\left(-8\right)}{2}$$

Multiply 3 and -8 to get -24.

$$360+1.6x<400+\frac{3}{2}x+\frac{-24}{2}$$

Divide -24 by 2 to get -12.

$$360+1.6x<400+\frac{3}{2}x-12$$

Subtract 12 from 400 to get 388.

$$360+1.6x<388+\frac{3}{2}x$$

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

$$360+1.6x-\frac{3}{2}x<388$$

Combine 1.6x and -\frac{3}{2}x to get \frac{1}{10}x.

$$360+\frac{1}{10}x<388$$

Subtract 360 from both sides.

$$\frac{1}{10}x<388-360$$

Subtract 360 from 388 to get 28.

$$\frac{1}{10}x<28$$

Multiply both sides by 10, the reciprocal of \frac{1}{10}. Since \frac{1}{10} is positive, the inequality direction remains the same.

$$x<28\times 10$$

Multiply 28 and 10 to get 280.

$$x<280$$