Solve 80-(2000-120a/80+a)geq15

$$80-( \frac{ 2000-120a }{ 80 } +a) \geq 15$$

Solve for a

$$a\geq -80$$

Solution Steps

Multiply both sides of the equation by 80. Since 80 is positive, the inequality direction remains the same.

$$6400-80\left(\frac{2000-120a}{80}+a\right)\geq 1200$$

Divide each term of 2000-120a by 80 to get 25-\frac{3}{2}a.

$$6400-80\left(25-\frac{3}{2}a+a\right)\geq 1200$$

Combine -\frac{3}{2}a and a to get -\frac{1}{2}a.

$$6400-80\left(25-\frac{1}{2}a\right)\geq 1200$$

Use the distributive property to multiply -80 by 25-\frac{1}{2}a.

$$6400-2000-80\left(-\frac{1}{2}\right)a\geq 1200$$

Express -80\left(-\frac{1}{2}\right) as a single fraction.

$$6400-2000+\frac{-80\left(-1\right)}{2}a\geq 1200$$

Multiply -80 and -1 to get 80.

$$6400-2000+\frac{80}{2}a\geq 1200$$

Divide 80 by 2 to get 40.

$$6400-2000+40a\geq 1200$$

Subtract 2000 from 6400 to get 4400.

$$4400+40a\geq 1200$$

Subtract 4400 from both sides.

$$40a\geq 1200-4400$$

Subtract 4400 from 1200 to get -3200.

$$40a\geq -3200$$

Divide both sides by 40. Since 40 is positive, the inequality direction remains the same.

$$a\geq \frac{-3200}{40}$$

Divide -3200 by 40 to get -80.

$$a\geq -80$$