Solve 30a+1-300a/200*24leq600

$$30 a + \frac { 1 - 300 a } { 200 } \times 24 \leq 600$$

Solve for a

$$a\geq -\frac{4999}{50}$$

Solution Steps

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

$$6000a+\left(1-300a\right)\times 24\leq 120000$$

Use the distributive property to multiply 1-300a by 24.

$$6000a+24-7200a\leq 120000$$

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

$$-1200a+24\leq 120000$$

Subtract 24 from both sides.

$$-1200a\leq 120000-24$$

Subtract 24 from 120000 to get 119976.

$$-1200a\leq 119976$$

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

$$a\geq \frac{119976}{-1200}$$

Reduce the fraction \frac{119976}{-1200} to lowest terms by extracting and canceling out 24.

$$a\geq -\frac{4999}{50}$$