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)

Answer 1

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 find the range of temperature in this town. (4 points)

Answer 2

@Phi can you help?

Answer 3

did you try e.g. part A ?

Answer 4

im confused with the information given before part A the i and upside down question marks do those mean anything?

Answer 5

I think that is a garbled degree sign
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.

Answer 6

so could the compound inequality be
14>3x+2 double my answer and subtract by 7?

Answer 7

12>3x
4>x
8-7>-11
-1>-11

Answer 8

ok, on the first statement
14>3x+2

the second statement is a completely separate statement (that is also true)
Twice the temperature minus 7 is greater than -11 C.

do the same thing: use x for the temp.

Answer 9

insert 4 in for x? or just keep it as x

Answer 10

we are not simplifying (yet), just writing down the relation

Answer 11

2x-7>-11

Answer 12

now simplify both statements (separately)

Answer 13

x<4 will be the first one second one is
x<-2

Answer 14

re-do the second one

Answer 15

2x-7>-11
2x>-4
x>-2

Answer 16

flipped the sign on mistake first time

Answer 17

much better.

so the solution are all x's bigger than -2 and less than 4
we could write it as
-2 < x < 4

Answer 18

and that would be the compound inequality?

Answer 19

I think A is just the original two equations (before simplifying)
14>3x+2
2x-7>-11

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

you solved and got
-2 < x < 4

is x allowed to be 5 ?

Answer 20

sorry having internet problems no x is not alowed to be 5 because
5 isn't less than 4

Answer 21

yes, OS is acting up.

now part C.

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 find the range of temperature in this town.

Any ideas?

Answer 22

not sure how i would write that as an inequality would it be 3<4 ?

Answer 23

the temperature (call it x) is within 4 degrees of the average.

the average is 3

so
x is within 4 degrees of 3

before writing the relation, can you figure out the upper and lower bounds for x ?

Answer 24

-1,0,1,2
4,5,6,7?

Answer 25

ok, but we allow fractional temps... so just list the lower temp and upper temp

-1 is the lowest
7 is the highest

now write the relation

Answer 26

-1<3<7

Answer 27

in other words x is bigger than -1 and x is less than 7

there is another way to write this, which uses absolute values
x is within 4 deg of 3 means the "distance" from 3 to x is less than 4
the "distance" is |x-3|

and we can write
|x-3| < 4

Answer 28

that last part was an "oh, by the way"
nice to know, but not needed for this question.

Answer 29

ahh ok lol thought i had to put it in that form so would i need to put it as
-1<3<7 or
-1<x<7

Answer 30

the first is a statement of fact (3 is bigger than -1 and less than 7)

the second says "x" (whatever "x" is) is between -1 and 7
if we say up front , "x" is the temperature, then this second statement means:
the temperature is always between -1 and 7

Answer 31

and its simplified as much as possible?