Solve (1-0.5)x-(0.5-0.3)(200-x)>2000

$$(1-0.5)x-(0.5-0.3)(200-x) > 2000$$

Solve for x

$$x>\frac{20400}{7}$$

Solution Steps

Subtract 0.5 from 1 to get 0.5.

$$0.5x-\left(0.5-0.3\right)\left(200-x\right)>2000$$

Subtract 0.3 from 0.5 to get 0.2.

$$0.5x-0.2\left(200-x\right)>2000$$

Use the distributive property to multiply -0.2 by 200-x.

$$0.5x-40+0.2x>2000$$

Combine 0.5x and 0.2x to get 0.7x.

$$0.7x-40>2000$$

Add 40 to both sides.

$$0.7x>2000+40$$

Add 2000 and 40 to get 2040.

$$0.7x>2040$$

Divide both sides by 0.7. Since 0.7 is positive, the inequality direction remains the same.

$$x>\frac{2040}{0.7}$$

Expand \frac{2040}{0.7} by multiplying both numerator and the denominator by 10.

$$x>\frac{20400}{7}$$