Question

Solve for z. -18z-9(-z-10)>3(-7z-18)

Write your answer with z first, followed by an inequality symbol.

Answer 1

To solve the inequality -18z-9(-z-10)>3(-7z-18) for z, distribute and combine like terms on each side before isolating z and solving the inequality. The solution is z>-12.

Step-by-step explanation:

To solve the inequality -18z-9(-z-10)>3(-7z-18) for z, we need to simplify the expression and isolate z.

1. Distribute -9 to -z-10 to get 9z+90.
2. Distribute 3 to -7z-18 to get -21z-54.
3. Combine like terms on each side of the inequality. On the left side, we have -18z+9z+90. Simplify this to get -9z+90. On the right side, we have -21z-54.
4. Add 21z to both sides to eliminate the -21z on the right side. This gives us -9z+21z+90>-54.
5. Combine like terms on the left side to get 12z+90>-54.
6. Subtract 90 from both sides to eliminate the 90 on the left side. This gives us 12z>-144.
7. Finally, divide both sides by 12 to solve for z. This gives us z>-12.

Therefore, the solution to the inequality is z>-12.