Question

http://prntscr.com/laybia

Answer 1

@Vocaloid

Answer 2

generally if you have a value that is at most "a" units from "b" you can write this as

|x - b| < a

so applying this to your problem

if the price (x) is at most $1.50 from $9.50 what would your inequality be?

Answer 3

I learned to do this a while ago but forgot :(

Answer 4

that absolute value inequality ?

Answer 5

yes, if you take the general logic

"generally if you have a value that is at most "a" units from "b" you can write this as

|x - b| < a"

and apply this to your problem to generate a similar inequality, what would it be?

Answer 6

you should read the problem and try to figure out what your "a" and "b" would be

Answer 7

a is 1.50
and b is 9.50

or other way around?

Answer 8

that's correct

so your inequality becomes

|x - 9.5| ≤ 1.5

(I changed < to ≤ because "as much as" is inclusive of the extreme values)

Answer 9

for b) do you know how you would go about solving this?

|x - 9.5| ≤ 1.5

Answer 10

−1.5≤x−9.5≤1.5

−1.5+9.5≤x≤1.5+9.5

8≤x≤11

Answer 11

good

so for c) any ideas how to graph this?

Answer 12

not sure lol

Answer 13

well "8≤x≤11" means x is greater than/equal to 8 but also less than/equal to 11

so we put two closed circles on 8 and 11 and graph the values in between

Answer 14

make sure to label the number line appropriately

then for d) it's straightforward, if x represents the hourly wages, then the inequality 8≤x≤11 means the hourly wages can be anywhere between 8$-11$/hour inclusive

Answer 15

http://prntscr.com/laygw1

Answer 16

same logic as last time

|x - b| ≤ a; where x is within "a" units of "b"

if the truffle count is always within 2 units of 20 what would your inequality be?

Answer 17

|x - 2| ≤ 20

Answer 18

almost
x is within "a" units of "b"
if x is within 2 units of 20 the inequality becomes, then a = 2 and b = 20 giving us

|x - 20| ≤ 2
then for b) just solve this inequality

Answer 19

−2≤x−20≤2

−2+20≤x≤2+20

18≤x≤22

Answer 20

awesome, so that's it

Answer 21

http://prntscr.com/layi8i

Answer 22

thats part c and d^

Answer 23

well for the graphing it's pretty much the same as last time just with 18≤x≤22 18 and 22 instead of 8 and 11

for d) again, applying the numbers to the actual problem, the truffle count is always between 18 and 22 inclusive

Answer 24

http://prntscr.com/layjji

Answer 25

same logic as last time

if the run time is always within 1.25 of 8.5 minutes what's your inequality?

Answer 26

|x - 1.25| ≤ 8.5

Answer 27

almost

the set value (in this case, 8.5 minutes) will always be on the inside of the inequality while the range "1.25 minutes" will be on the outside of the inequality
|x - 8.5| ≤ 1.25

Answer 28

try b, c, and d using the previous examples as a guide, I'll help you out if you get stuck

Answer 29

can you show me how to do the graph again?

Answer 30

notice how this is the graph of 8 ≤ x ≤ 11

try to apply the same logic to your inequality

Answer 31

is this right http://prntscr.com/layli6

Answer 32

almost just change the < to ≤ if you can because 7.25 minutes and 9.25 minutes would be included in the solution set the way it is phrased

Answer 33

so if your solution is 7.25 ≤ x ≤ 9.25 that means you plot 7.25 and 9.25 on a number line and connect them horizontally to represent that x can be anywhere between 7.25 and 9.25 inclusive

for d) what do you think this means in terms of the actual problem? what do 7.25 and 9.25 represent?