A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
In a certain town the temperature, x in degrees Celsius on a certain day is described by two statements:
If 3 times the temperature is increased by 2, the temperature is still less than 14°C.
Twice the temperature minus 7 is greater than 11°C.
Part A: Create a compound inequality to represent the temperature range. (3 points)
Part B: Can the temperature in this town be 5°C? Justify your answer by solving the inequalities in Part A. (3 points)
Part C: The average temperature in another town is 3°C, but the actual temperature is within 4°C of the average. Write and
anonymous
 one year ago
In a certain town the temperature, x in degrees Celsius on a certain day is described by two statements: If 3 times the temperature is increased by 2, the temperature is still less than 14°C. Twice the temperature minus 7 is greater than 11°C. Part A: Create a compound inequality to represent the temperature range. (3 points) Part B: Can the temperature in this town be 5°C? Justify your answer by solving the inequalities in Part A. (3 points) Part C: The average temperature in another town is 3°C, but the actual temperature is within 4°C of the average. Write and

This Question is Open

Ciarán95
 one year ago
Best ResponseYou've already chosen the best response.1\(\large Hi~...~Welcome~to~OpenStudy~!~:)\) A compound inequality is one which contains not just one inequality sign, but two. For example, you may be familiar with the notation: \[x < 2\] meaning that we know that our unknown value 'x' is less than 2. However, let's say that we also know that for this same value of 'x': \[x > 1\] (i.e. the value of 'x' is greater than 1) Combining these two pieces of information, we can use the following notation: \[1 < x < 2\] meaning that we know that the value of 'x' is between that of 1 and 2. This would be a compound inequality, and that's what we're looking to set up in Part A. Part A: We're told in the question to let x be the temperature on a certain day in a certain town (in degree Celsius). Were also told: 1.)If 3 times the temperature is increased by 2, the temperature is still less than 14°C. 2.)Twice the temperature minus 7 is greater than 11°C. We can represent these two pieces of information as two separate algebraic inequalities in terms of our unknown value x: \[1.)3x + 2 < 14\] \[2.) 2x  7 > 11\] So, to combine these and form our compound inequality, we'll try and get 'x' on its own in the two individually first. In doing, this, we can simply treat the '<' and '>' signs as if they were an '=' sign in this case, like if we were dealing with and equation. 1.) 3x + 2 < 14 Subtracting 2 from both sides, we get: 3x < 14  2, implying 3x < 12 Now, dividing each side by 3 to get x on its own, we're left with: x < 4 That's one half of our compound inequality completed. 2.) 2x  7 > 11 Getting x on its own as in 1.) above: 2x > 11 + 7, implying 2x > 4, implying x > 2 So, we now know that the temperature in the town on a given day will be less that 4 degrees Celsius AND greater than 2 degrees Celsius. Combining these pieces of information together, we're left with the following compound inequality for x (i.e. the range of possible temperatures in the town): \[2 < x < 4\] Part B: The final compound inequality we've created in Part A. should automatically tell us whether a temperature of 5 degrees is possible, based on the information we're given. Part C: The last part of the question appears to be cut off @saltychickk, so I can't really help you with that part!

radar
 one year ago
Best ResponseYou've already chosen the best response.0This was an excellent response. Very detailed and in a logical order. Certainly worthy of a medal.

radar
 one year ago
Best ResponseYou've already chosen the best response.0@Ciarán95 When I pose a problem, I would welcome an explanation such as this.

Ciarán95
 one year ago
Best ResponseYou've already chosen the best response.1Thanks so much @radar :) Hopefully if you have a problem I might be able to help you out sometime, but there are so many great contributors on OpenStudy!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.