Solve 4160-3000+15x+10.5(138-x)geq900

$$4160 - 3000 + 15 x + 10.5 ( 138 - x ) \geq 900$$

Solve for x

$$x\geq -\frac{3418}{9}$$

Solution Steps

Subtract 3000 from 4160 to get 1160.

$$1160+15x+10.5\left(138-x\right)\geq 900$$

Use the distributive property to multiply 10.5 by 138-x.

$$1160+15x+1449-10.5x\geq 900$$

Add 1160 and 1449 to get 2609.

$$2609+15x-10.5x\geq 900$$

Combine 15x and -10.5x to get 4.5x.

$$2609+4.5x\geq 900$$

Subtract 2609 from both sides.

$$4.5x\geq 900-2609$$

Subtract 2609 from 900 to get -1709.

$$4.5x\geq -1709$$

Divide both sides by 4.5. Since 4.5 is positive, the inequality direction remains the same.

$$x\geq \frac{-1709}{4.5}$$

Expand \frac{-1709}{4.5} by multiplying both numerator and the denominator by 10.

$$x\geq \frac{-17090}{45}$$

Reduce the fraction \frac{-17090}{45} to lowest terms by extracting and canceling out 5.

$$x\geq -\frac{3418}{9}$$