Solve x/100*05+(3600-x)div200*12<40

$$\frac{ x }{ 100 } \times 05+(3600-x) \div 200 \times 12 < 40$$

Solve for x

$$x>\frac{8800}{3}$$

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.

$$2x\times 0\times 5+\left(3600-x\right)\times 12<8000$$

Multiply 2 and 0 to get 0.

$$0x\times 5+\left(3600-x\right)\times 12<8000$$

Multiply 0 and 5 to get 0.

$$0x+\left(3600-x\right)\times 12<8000$$

Anything times zero gives zero.

$$0+\left(3600-x\right)\times 12<8000$$

Use the distributive property to multiply 3600-x by 12.

$$0+43200-12x<8000$$

Add 0 and 43200 to get 43200.

$$43200-12x<8000$$

Subtract 43200 from both sides.

$$-12x<8000-43200$$

Subtract 43200 from 8000 to get -35200.

$$-12x<-35200$$

Divide both sides by -12. Since -12 is negative, the inequality direction is changed.

$$x>\frac{-35200}{-12}$$

Reduce the fraction \frac{-35200}{-12} to lowest terms by extracting and canceling out -4.

$$x>\frac{8800}{3}$$