Solve 6000-(3007000)a/600*700+(700+500)aleq8000

$$\frac { 6000 - ( 3007000 ) a } { 600 } \times 700 + ( 700 + 500 ) a \leq 8000$$

Solve for a

$$a\geq -\frac{30}{105209}$$

Solution Steps

Multiply both sides of the equation by 600. Since 600 is positive, the inequality direction remains the same.

$$\left(6000-3007000a\right)\times 700+600\left(700+500\right)a\leq 4800000$$

Use the distributive property to multiply 6000-3007000a by 700.

$$4200000-2104900000a+600\left(700+500\right)a\leq 4800000$$

Add 700 and 500 to get 1200.

$$4200000-2104900000a+600\times 1200a\leq 4800000$$

Multiply 600 and 1200 to get 720000.

$$4200000-2104900000a+720000a\leq 4800000$$

Combine -2104900000a and 720000a to get -2104180000a.

$$4200000-2104180000a\leq 4800000$$

Subtract 4200000 from both sides.

$$-2104180000a\leq 4800000-4200000$$

Subtract 4200000 from 4800000 to get 600000.

$$-2104180000a\leq 600000$$

Divide both sides by -2104180000. Since -2104180000 is negative, the inequality direction is changed.

$$a\geq \frac{600000}{-2104180000}$$

Reduce the fraction \frac{600000}{-2104180000} to lowest terms by extracting and canceling out 20000.

$$a\geq -\frac{30}{105209}$$