Solve x/100*0.5+(3600-x)div200*1.2<40

$$\frac{ x }{ 100 } \times 0.5+(3600-x) \div 200 \times 1.2 < 40$$

Solve for x

$$x>-18400$$

Solution Steps

Multiply both sides of the equation by 200, the least common multiple of 100,200. Since 200 is positive, the inequality direction remains the same.

$$2x\times 0.5+\left(3600-x\right)\times 1.2<8000$$

Multiply 2 and 0.5 to get 1.

$$x+\left(3600-x\right)\times 1.2<8000$$

Use the distributive property to multiply 3600-x by 1.2.

$$x+4320-1.2x<8000$$

Combine x and -1.2x to get -0.2x.

$$-0.2x+4320<8000$$

Subtract 4320 from both sides.

$$-0.2x<8000-4320$$

Subtract 4320 from 8000 to get 3680.

$$-0.2x<3680$$

Divide both sides by -0.2. Since -0.2 is negative, the inequality direction is changed.

$$x>\frac{3680}{-0.2}$$

Expand \frac{3680}{-0.2} by multiplying both numerator and the denominator by 10.

$$x>\frac{36800}{-2}$$

Divide 36800 by -2 to get -18400.

$$x>-18400$$