Question

1. joe ran 3 miles yesterday and wants to run at least 12 miles this week. write an inequality that can be used to determine the additional number of days joe must run this week if each run is 3 miles. then solve the inequality.

yesterday:
3 miles
additional days?
joes goal this week: run at least 12 miles

Explanation:

Step1: Define the variable

Let \( d \) be the number of additional days Joe runs. Each day he runs 3 miles, so the additional miles he runs is \( 3d \). He already ran 3 miles yesterday. His total miles should be at least 12, so the inequality is \( 3 + 3d \geq 12 \).

Step2: Solve the inequality

Subtract 3 from both sides: \( 3d \geq 12 - 3 \)
Simplify: \( 3d \geq 9 \)

Step3: Divide both sides by 3

\( d \geq \frac{9}{3} \)
Simplify: \( d \geq 3 \)

Answer:

The inequality is \( 3 + 3d \geq 12 \) (where \( d \) is the number of additional days), and the solution is \( d \geq 3 \), meaning Joe must run for at least 3 additional days.