Question

WILL FAN AND GIVE MEDAL! Do you mind helping me through this process? I already took the quiz and know the answer, but guessed on it. How was the answer found?

Answer 1

The minimum and maximum temperature on a cold day in Lollypop Town can be modeled by the equation below:

2|x − 6| + 14 = 38

What are the minimum and maximum temperatures for this day?

x = −9, x = 21

x = −6, x = 18

x = 6, x = −18

No solution
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The answer is B.

Answer 2

You need to get |x-6| isolated on one side of the equation. Do you know how?

Answer 3

No, but I guess that's why I don't understand how to do this haha (:

Answer 4

OK lets start.
First lets subtract -14 from both sides of the equation. What do you end up with?

Answer 5

Like 2 and 38? sorry, new to this

Answer 6

No prob,,if we subtract 14 from both sides of the equation
2|x-6|+14-14 = 38-14
we end up with
2|x-6| = 24
Do you see?

Answer 7

What is the reason for doing that?

Answer 8

When solving for unknown variables in this case (x) you need to get the unknown on one side of the equation by itself.

Answer 9

Ok yea i get it.

Answer 10

So we have 2|x-6| =24 Now we need to get rid of the 2. Any thoughts?

Answer 11

I really have no clue. /:

Answer 12

Divide both sides by 2...\[\frac{ 2|x-6| }{ 2 } = \frac{ 24 }{ 2 }\]

Answer 13

o you know what this will leave us witth?D

Answer 14

I feel like an idiot because a 5 year old could probably do this lol but what exactly am i dividing? like 24/2 or 2|x-6|/2 or? sorry

Answer 15

The 2's cancel out on the right side and 24/2 = 12 on the left so we end up with
|x-6|=12

Answer 16

Now to solve for absolute value equation |x-6|=12 we will always have two solutions. The way to solve them is to make your answer both positive and negative like so.

x-6 = 12 Solve for x
x-6 = -12 Solve for x

Answer 17

I get it now, thank you soooo much! :D

Answer 18

Actually no, I take it back... I don't get it ):

x would be 6 and -18? @nelsonjedi

Answer 19

Did I miss something? x is supposed to be -6 and 18.