Solve 5(3+z)>-3left(z+3right)

$$5(3+z) > -3 \left( z+3 \right)$$

Solve for z

$$z>-3$$

Solution Steps

Use the distributive property to multiply 5 by 3+z.

$$15+5z>-3\left(z+3\right)$$

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

$$15+5z>-3z-9$$

Add 3z to both sides.

$$15+5z+3z>-9$$

Combine 5z and 3z to get 8z.

$$15+8z>-9$$

Subtract 15 from both sides.

$$8z>-9-15$$

Subtract 15 from -9 to get -24.

$$8z>-24$$

Divide both sides by 8. Since 8 is positive, the inequality direction remains the same.

$$z>\frac{-24}{8}$$

Divide -24 by 8 to get -3.

$$z>-3$$