Solve (x-160)*200+(x-170)*400/100000geq0.2

$$\frac { ( x - 160 ) \times 200 + ( x - 170 ) \times 400 } { 100000 } \geq 0.2$$

Solve for x

$$x\geq 200$$

Solution Steps

Multiply both sides by 100000. Since 100000 is positive, the inequality direction remains the same.

$$\left(x-160\right)\times 200+\left(x-170\right)\times 400\geq 0.2\times 100000$$

Use the distributive property to multiply x-160 by 200.

$$200x-32000+\left(x-170\right)\times 400\geq 0.2\times 100000$$

Use the distributive property to multiply x-170 by 400.

$$200x-32000+400x-68000\geq 0.2\times 100000$$

Combine 200x and 400x to get 600x.

$$600x-32000-68000\geq 0.2\times 100000$$

Subtract 68000 from -32000 to get -100000.

$$600x-100000\geq 0.2\times 100000$$

Multiply 0.2 and 100000 to get 20000.

$$600x-100000\geq 20000$$

Add 100000 to both sides.

$$600x\geq 20000+100000$$

Add 20000 and 100000 to get 120000.

$$600x\geq 120000$$

Divide both sides by 600. Since 600 is positive, the inequality direction remains the same.

$$x\geq \frac{120000}{600}$$

Divide 120000 by 600 to get 200.

$$x\geq 200$$