Solve 40+0.5(c-140)>270+0.2(c-27

$$40 + 0.5 ( c - 140 ) > 270 + 0.2 ( c - 27$$

Solve for c

$$c>982$$

Solution Steps

Use the distributive property to multiply 0.5 by c-140.

$$40+0.5c-70>270+0.2\left(c-27\right)$$

Subtract 70 from 40 to get -30.

$$-30+0.5c>270+0.2\left(c-27\right)$$

Use the distributive property to multiply 0.2 by c-27.

$$-30+0.5c>270+0.2c-5.4$$

Subtract 5.4 from 270 to get 264.6.

$$-30+0.5c>264.6+0.2c$$

Subtract 0.2c from both sides.

$$-30+0.5c-0.2c>264.6$$

Combine 0.5c and -0.2c to get 0.3c.

$$-30+0.3c>264.6$$

Add 30 to both sides.

$$0.3c>264.6+30$$

Add 264.6 and 30 to get 294.6.

$$0.3c>294.6$$

Divide both sides by 0.3. Since 0.3 is positive, the inequality direction remains the same.

$$c>\frac{294.6}{0.3}$$

Expand \frac{294.6}{0.3} by multiplying both numerator and the denominator by 10.

$$c>\frac{2946}{3}$$

Divide 2946 by 3 to get 982.

$$c>982$$