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.

Part B: Can the temperature in this town be 5°C? Justify your answer by solving the inequalities in Part A.

Part C: The average temperature in another town is 3°C, but the actual temperature is within 4°C of the average. Write and solve an inequality to

Answer 1

I'm not sure what you mean by Part C, some of the question appears to have been cut off....

Let's consider the two statements and rewrite what they're saying in inequality form:
1.)If 3 times the temperature,x, is increased by 2 degrees Celsius, the temperature is still less than 14 degrees Celsius. We can write this as:
\[3x +2 <14\]
2.)Twice the temperature, minus 7 degrees Celsius, is greater than -11. Similarly, we can write:
\[2x -7 > -11\]

We now have two equations which can both be solved for x. The first inequality will give us
x < something and the second inequality x > something. The value x is representing in both inequalities is the same - it's referring to the temperature in a certain town on a certain day. So, we will now have a range of values that this temperature could possibly be:

something > x > something else

If 5 degrees Celsius is within this range, then we can say that it is a possible temperature for the town, based on the information we are given. If not, then we cannot say so based on what we are told.

Hopefully this should help you get started on A and B...good luck! :)

Answer 2

Sorry about Part C. This is what it says.:

The average temperature in another town is 3°C, but the actual temperature is within 4°C of the average. Write and solve an inequality to find the range of temperature in this town

Answer 3

The range part in C would look like this: 3 degrees minus 4 degrees for the low and then 3 degrees plus 4 degrees for the high. So the temps would feasibly fall within -1 and 7 to look like this as an inequality: -1<x<7

Answer 4

Part a and b is a final inequality of -2<x<4