Normal Household Voltage

[harpazo]

Section R.2
Algebra Essentials
Michael Sullivan
Textbook: College Algebra Edition 9

In other countries, normal household voltage is 220 volts. It is acceptable for the actual voltage x to differ from normal by at most 8 volts. A formula describes this is

|x - 220| ≤ 8

A. Show that a voltage of 214 volts is acceptable.

Solution:

|x - 220| ≤ 8

Let x = 214

|214 - 220| ≤ 8

| 6 | ≤ 8

6 ≤ 8...This is a true statement. I conclude that a voltage of 214 is acceptable.

B. Show that a voltage of 209 is not acceptable.

Solution:

|x - 220| ≤ 8

Let x = 209

|209 - 220| ≤ 8

| - 11 | ≤ 8

11 ≤ 8...This is false statement. I conclude that a voltage of 209 is NOT acceptable.

Do I understand this question correctly?

 

[tkhunny]

I think you have it!

 

[harpazo]

I think you have it!

I understand this to be an easy application but word problems will increase in complexity as I move on in the textbook from chapter to chapter and section to section.

 

[JeffM]

I am just happy that you are proceeding methodically and doing exercises. That is 90% of learning basic math.

 

[Steven G]

Since you only had to check two values your method was fine. Very good. But what if your job is to decide 8 hours a day if various voltages are acceptable or not.

Here is a better way to consider your problem
|x - 220| ≤ 8
-8 ≤ x - 220 ≤ 8
212 ≤ x ≤ 228
So you accept any voltage between 212 and 228

 

[pka]

|x - 220| ≤ 8
-8 ≤ x - 220 ≤ 8
212 ≤ x ≤ 228
So you accept any voltage between 212 and 228

Actually we accept any voltage from 212 to 228.
The word between actually means between so neither 212 nor 228 is included if you say "voltage between 212 and 228" .

 

[harpazo]

Thank you everyone for your input and ideas.