Solve 3(z-1)-2geqz+5(z+2)

$$3 ( z - 1 ) - 2 \geq z + 5 ( z + 2 )$$

Solve for z

$$z\leq -5$$

Solution Steps

Use the distributive property to multiply 3 by z-1.

$$3z-3-2\geq z+5\left(z+2\right)$$

Subtract 2 from -3 to get -5.

$$3z-5\geq z+5\left(z+2\right)$$

Use the distributive property to multiply 5 by z+2.

$$3z-5\geq z+5z+10$$

Combine z and 5z to get 6z.

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

Subtract 6z from both sides.

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

Combine 3z and -6z to get -3z.

$$-3z-5\geq 10$$

Add 5 to both sides.

$$-3z\geq 10+5$$

Add 10 and 5 to get 15.

$$-3z\geq 15$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$z\leq \frac{15}{-3}$$

Divide 15 by -3 to get -5.

$$z\leq -5$$