Solve 20(2.5x-600)+100*30*20geq8*10^4

$$20(2.5x-600)+100 \times 30 \times 20 \geq 8 \times { 10 }^{ 4 }$$

Solve for x

$$x\geq 640$$

Solution Steps

Use the distributive property to multiply 20 by 2.5x-600.

$$50x-12000+100\times 30\times 20\geq 8\times 10^{4}$$

Multiply 100 and 30 to get 3000.

$$50x-12000+3000\times 20\geq 8\times 10^{4}$$

Multiply 3000 and 20 to get 60000.

$$50x-12000+60000\geq 8\times 10^{4}$$

Add -12000 and 60000 to get 48000.

$$50x+48000\geq 8\times 10^{4}$$

Calculate 10 to the power of 4 and get 10000.

$$50x+48000\geq 8\times 10000$$

Multiply 8 and 10000 to get 80000.

$$50x+48000\geq 80000$$

Subtract 48000 from both sides.

$$50x\geq 80000-48000$$

Subtract 48000 from 80000 to get 32000.

$$50x\geq 32000$$

Divide both sides by 50. Since 50 is positive, the inequality direction remains the same.

$$x\geq \frac{32000}{50}$$

Divide 32000 by 50 to get 640.

$$x\geq 640$$