Solve 0.75*400x+0.9*360*(80-x)geq280000

$$0.75 \times 400x+0.9 \times 360 \times (80-x) \geq 280000$$

Solve for x

$$x\leq -\frac{31760}{3}$$

Solution Steps

Multiply 0.75 and 400 to get 300.

$$300x+0.9\times 360\left(80-x\right)\geq 280000$$

Multiply 0.9 and 360 to get 324.

$$300x+324\left(80-x\right)\geq 280000$$

Use the distributive property to multiply 324 by 80-x.

$$300x+25920-324x\geq 280000$$

Combine 300x and -324x to get -24x.

$$-24x+25920\geq 280000$$

Subtract 25920 from both sides.

$$-24x\geq 280000-25920$$

Subtract 25920 from 280000 to get 254080.

$$-24x\geq 254080$$

Divide both sides by -24. Since -24 is negative, the inequality direction is changed.

$$x\leq \frac{254080}{-24}$$

Reduce the fraction \frac{254080}{-24} to lowest terms by extracting and canceling out 8.

$$x\leq -\frac{31760}{3}$$