Solve 12x+6(10-x)geq75

$$12x+6(10-x) \geq 75$$

Solve for x

$$x\geq \frac{5}{2}$$

Solution Steps

Use the distributive property to multiply 6 by 10-x.

$$12x+60-6x\geq 75$$

Combine 12x and -6x to get 6x.

$$6x+60\geq 75$$

Subtract 60 from both sides.

$$6x\geq 75-60$$

Subtract 60 from 75 to get 15.

$$6x\geq 15$$

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

$$x\geq \frac{15}{6}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$x\geq \frac{5}{2}$$