Solve 30a+5500-300a/200*24leq600

$$30 a + \frac { 5500 - 300 a } { 200 } \times 24 \leq 600$$

Solve for a

$$a\geq 10$$

Solution Steps

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

$$6000a+\left(5500-300a\right)\times 24\leq 120000$$

Use the distributive property to multiply 5500-300a by 24.

$$6000a+132000-7200a\leq 120000$$

Combine 6000a and -7200a to get -1200a.

$$-1200a+132000\leq 120000$$

Subtract 132000 from both sides.

$$-1200a\leq 120000-132000$$

Subtract 132000 from 120000 to get -12000.

$$-1200a\leq -12000$$

Divide both sides by -1200. Since -1200 is negative, the inequality direction is changed.

$$a\geq \frac{-12000}{-1200}$$

Divide -12000 by -1200 to get 10.

$$a\geq 10$$