Question

Graph the solution of the inequality.
14 ≤ 2t + 18 < 20





@phi

Answer 1

1. http://www.wolframalpha.com/input/?i=14+ …

2. (-3,-5,-7)

Answer 2

14 ≤ 2t + 18 < 20

there is only one variable ( the t), so expect a number line.

do you know algebra ?
do the two equations separately:
first 2t + 18 < 20
add -18 to both sides. what do you get ?

Answer 3

2

Answer 4

like this
2t +18 -18 < 20 -18
what is 18-18 ?
what is 20-18?
can you simplify this ?

Answer 5

2t + 18 < 20
becomes
2t < 2 (after we add -18 to BOTH sides) and simplify
now divide both sides by 2:

2t/2 < 2/2
what do you get after simplifying ?

Answer 6

1

Answer 7

what about the left side ?

Answer 8

its just t now

Answer 9

and the symbol in between ?

Answer 10

=

Answer 11

t = 1

Answer 12

no mysterious changes.... it is still <

we start with
2t < 2
and it becomes
t < 1

Answer 13

d?

Answer 14

oops.
I meant
t < 1 means open circle at 1 and shaded to smaller numbers (toward 0 )

Answer 15

to graph (this part) the < means put an open circle at 1
if it were t ≤ 1 put a solid circle at 1
this is like the rules for solid lines and dashed lines in your other problem

t < 1 means open circle at 1 and shaded to smaller numbers (toward 0 )

now do the other part of the problem
14 ≤ 2t + 18

Answer 16

d?

Answer 17

I made a typo t < 1 means an OPEN CIRCLE at 1

Answer 18

So you have only 2 choices with an open circle at 1

you want the choice where the solid line is less than 1

Answer 19

a?

Answer 20

yes.

If we had more choices that showed an open circle at 1 and a solid line to the left of the circle, we would check the other part of the equation
14 ≤ 2t + 18

notice that this part has ≤ so we will use a solid circle . But we have to do the algebra to figure out exactly where the solid circle goes. (But based on choice A it will go at -2)

Answer 21

you can practice your algebra
14 ≤ 2t +18
add -18 to both sides
14-18 ≤ 2t+18-18
or
-4 ≤ 2t
divide both sides by 2
-2 ≤ t
yes, it is a solid circle at -2 and the line goes toward bigger numbers

Answer 22

If you are not sure which way to draw the solid line when looking at
-2 ≤ t
pick a number like 1 for t
-2 ≤ 1 is this true. Yes. 1 is bigger than or equal to -2.
That means draw the solid line on the side that has +1 (to the right of -2)

Answer 23

c?

Answer 24

@phi ???

Answer 25

why do you say c ?

read over the posts.

Answer 26

my sister said

Answer 27

so obvious it b since thats the last one