To solve the inequality 8z + 3 < 2z + 51, follow these steps:
- Isolate the variable: Start by moving all the terms involving z to one side of the inequality and the constant terms to the other side. This allows us to isolate z.
- Subtract 2z from both sides:
8z + 3 - 2z < 2z + 51 - 2z
6z + 3 < 51 - Subtract 3 from both sides:
6z + 3 - 3 < 51 - 3
6z < 48 - Divide both sides by 6:
z < 48 / 6
z < 8
Thus, the solution to the inequality 8z + 3 < 2z + 51 is z < 8.
To visualize this solution, you can represent it on a number line. All the numbers to the left of 8 (not including 8 itself) are solutions to the inequality.
In summary, the steps taken are:
- Move terms involving z to one side
- Combine like terms
- Isolate z by performing arithmetic operations
This method can be applied to solve similar inequalities effectively.