Final answer:
To solve the inequality −3+5(z−3)<5z+1+10z, we simplify both sides to get 5z − 18 < 15z + 1, then isolate z to find z > −1.9.
Step-by-step explanation:
The student is asking for a solution to the inequality −3+5(z−3)<5z+1+10z. To solve this inequality, we need to collect like terms and simplify both sides of the inequality.
First, we expand the terms on the left side: −3 + 5z − 15.
Combine like terms on the left side: 5z − 18.
On the right side, combine like terms: 15z + 1.
Subtract 5z from both sides to get all the z terms on one side: − 18 < 10z + 1.
Subtract 1 from both sides to isolate the terms with z: − 19 < 10z.
Finally, divide by 10 to solve for z: z > −1.9.
The solution to the inequality is z > −1.9.