Solve 2(2z+3)geq2z+18

$$2 ( 2 z + 3 ) \geq 2 z + 18$$

Solve for z

$$z\geq 6$$

Solution Steps

Use the distributive property to multiply 2 by 2z+3.

$$4z+6\geq 2z+18$$

Subtract 2z from both sides.

$$4z+6-2z\geq 18$$

Combine 4z and -2z to get 2z.

$$2z+6\geq 18$$

Subtract 6 from both sides.

$$2z\geq 18-6$$

Subtract 6 from 18 to get 12.

$$2z\geq 12$$

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

$$z\geq \frac{12}{2}$$

Divide 12 by 2 to get 6.

$$z\geq 6$$