Question

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

Answer 1

help?

Answer 2

\(\large Hi~...~Welcome~to~OpenStudy~!~:)\)

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!

Answer 3

This was an excellent response. Very detailed and in a logical order. Certainly worthy of a medal.

Answer 4

@Ciarán95 When I pose a problem, I would welcome an explanation such as this.

Answer 5

Thanks 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!