Solve -3(u+9)+21geq5(2-u)

$$- 3 ( u + 9 ) + 21 \geq 5 ( 2 - u )$$

Solve for u

$$u\geq 8$$

Solution Steps

Use the distributive property to multiply -3 by u+9.

$$-3u-27+21\geq 5\left(2-u\right)$$

Add -27 and 21 to get -6.

$$-3u-6\geq 5\left(2-u\right)$$

Use the distributive property to multiply 5 by 2-u.

$$-3u-6\geq 10-5u$$

Add 5u to both sides.

$$-3u-6+5u\geq 10$$

Combine -3u and 5u to get 2u.

$$2u-6\geq 10$$

Add 6 to both sides.

$$2u\geq 10+6$$

Add 10 and 6 to get 16.

$$2u\geq 16$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$u\geq \frac{16}{2}$$

Divide 16 by 2 to get 8.

$$u\geq 8$$