Solve 0.6x+0.06x+0.6(30-x)+0.05(30-x)geq19.62

$$0.6x+0.06x+0.6(30-x)+0.05(30-x) \geq 19.62$$

Solve for x

$$x\geq 12$$

Solution Steps

Combine 0.6x and 0.06x to get 0.66x.

$$0.66x+0.6\left(30-x\right)+0.05\left(30-x\right)\geq 19.62$$

Use the distributive property to multiply 0.6 by 30-x.

$$0.66x+18-0.6x+0.05\left(30-x\right)\geq 19.62$$

Combine 0.66x and -0.6x to get 0.06x.

$$0.06x+18+0.05\left(30-x\right)\geq 19.62$$

Use the distributive property to multiply 0.05 by 30-x.

$$0.06x+18+1.5-0.05x\geq 19.62$$

Add 18 and 1.5 to get 19.5.

$$0.06x+19.5-0.05x\geq 19.62$$

Combine 0.06x and -0.05x to get 0.01x.

$$0.01x+19.5\geq 19.62$$

Subtract 19.5 from both sides.

$$0.01x\geq 19.62-19.5$$

Subtract 19.5 from 19.62 to get 0.12.

$$0.01x\geq 0.12$$

Divide both sides by 0.01. Since 0.01 is positive, the inequality direction remains the same.

$$x\geq \frac{0.12}{0.01}$$

Expand \frac{0.12}{0.01} by multiplying both numerator and the denominator by 100. Anything divided by one gives itself.

$$x\geq 12$$