Question

Part A

Joseph runs 2 miles on Monday. Each day after that, he runs the same 1 mile route every morning. His goal is to run at least 6 miles
by the end of the week. Which inequality represents the least number of days after Monday that Joseph needs to run to reach his goal?

Answer 1

Sine he runs 2 miles on Monday, we already have a +2.

Then, he runs by a constant rate of 1, which is the constant rate of change per day.

Let x represent the number of days he runs and y the total amount of miles he runs. Now, the equation is y = x + 2

However, he needs to run at least 6 miles. At least means greater than or equal to. The values for y can be greater than 6, or equal to 6.

y ≥ 6

y = x + 2

Now substitute x + 2 for y.

x + 2 ≥ 6

Subtract 2.

x ≥ 4

This is the inequality. He has to run for at least 4 days.