Final answer:
To solve the inequality 4z > 17, divide both sides by 4 to get z > 4.25, which means all numbers greater than 4.25 are solutions.
Step-by-step explanation:
To solve the inequality 4z > 17, you need to isolate the variable 'z' on one side. This can be done by dividing both sides of the inequality by 4, the coefficient of z. Doing this calculation, we get:
4z / 4 > 17 / 4
z > 4.25
This means that any number greater than 4.25 is a solution to the inequality. In terms of number lines, you would shade the portion that is to the right of 4.25, indicating all the values that are greater than 4.25 satisfy the inequality. Remember that since this is an inequality, rather than a strict equation, the solutions are not limited to a single number, but to a range of numbers.