Question

In a certain town, the barometric inches of air pressure, x, on a certain day is described by two statements:


If 3 times the air pressure is increased by 2, the pressure is still less than 92 inches.
Twice the air pressure minus 39 is greater than 11 inches.


Part A: Create a compound inequality to represent the air pressure range.

Part B: Can the air pressure in this town be 24 inches? Justify your answer by solving the inequalities in Part A.

Part C: The average air pressure in another town is 29 inches but the actual pressure is within 4 inches of the average.

Answer 1

Write and solve an inequality to find the range of air pressure in this town

Answer 2

@Hero i believe A is 3x+2<92 and 2x-39>11

Answer 3

@ganeshie8 am i right

Answer 4

can you help me do the rest

Answer 5

for part B,
put x = 24 and see if it satisfies both the inequalities

Answer 6

3x+2<92 and 2x-39>11

plugin x = 24

3(24)+2 < 92 and 2(24)-39 > 11
72+2 < 92 and 48-39 > 11
74 < 92 and 9 > 11
TRUE and \(\color{red}{FALSE}\)

Answer 7

that means x = 24, doesnt satisfy the second inequality.
so what do u conclude ?

Answer 8

that one can work and the other cant

Answer 9

Part C: The average air pressure in another town is 29 inches but the actual pressure is within 4 inches of the average.

Answer 10

say the average air pressure is \(x\) :

\(x - 4 < 29\) and \(x+4 > 29\)

Answer 11

solve them

Answer 12

how do i solve it

Answer 13

solve \(x\) in each inequality

Answer 14

how

Answer 15

\(x - 4 < 29\)

add 4 both sides, what do u get ?

Answer 16

x<33

Answer 17

thats it ! so x must be less than 33, thats ur upper limit

Answer 18

similarly solve the other inequality

Answer 19

\(x+4 > 29\)

subtract 4 both sides

Answer 20

x>25

Answer 21

yes :

x < 33 and x > 25

that means the range is 25<x<33

Answer 22

x must be between 25 and 33

Answer 23

so thats c

Answer 24

thank you