Question

Absolute Value Equation:
A group of students ran a mile with an average time of 9 minutes. Individual times were no more than 3 minutes higher or lower than the average. Write an absolute value equation to model this situation, and solve the equation to determine the range of times.

Answer 1

Let x be a student's mile time in minutes

The distance from x to the average is |x-9| since absolute value is used to measure distance on a number line.

Let's say x = 7 minutes, this means |x-9| = |7-9| = 2 tells us the time value x = 7 is two units away from the average.

We're told that the highest and lowest times were no further than 3 units away from the average.

This must mean we have the absolute value equation
|x-9| = 3

Solving this equation for x leads to the highest and lowest times possible.

Answer 2

i dont know how to solve it

Answer 3

You use the rule that |x| = k turns into x = -k or x = k

Answer 4

In this case,
|x-9| = 3
turns into the two equations
x-9 = 3 or x - 9 = -3

Answer 5

woahh what. i dont understand this

Answer 6

what do you get when you solve x-9 = 3

Answer 7

12?

Answer 8

yes, and how about x-9 = -3 ?

Answer 9

6?

Answer 10

yes, so 6 is the lowest time and 12 is the highest time

We can see this with a number line

Answer 11

sure?!

the Qu posits that:

\(\bar t = 9 = \dfrac{\Sigma t_i}{N}\)

with:

\(\bar t - 3 < t_i < \bar t + 3 \qquad \forall t\)