Question

If y=-7 Which solution is true?

A.
y + 5 > –2

B.
y + 5 ≥ –2

C.
y + 5 < –2

D.
y + 5 ≤ –2

Answer 1

nevermind. it has the weird questionmark symbols

Answer 2

refresh (reload) the page

Answer 3

it's B so y>=-7

Answer 4

but what would the difference between B and D be? they are both equal to, right? B is greater than or equal to, D is less than or equal to. they both have equal to!

Answer 5

@phi

Answer 6

@felavin

Answer 7

both B and D are true. So either you mark both, or the question has a mistake.

Answer 8

would the answer matter if there was a number line with it? i'll attatch a screen shot.

Answer 9

i just said y=-7 since thats where it was on the line..... i think

Answer 10

the number line is a different question. It has an open circle at -7 which means -7 is NOT part of the solution. (A solid dot would include -7)
it shows numbers bigger than -7 are part of the solution (the solid red arrow pointing to the right)

so the answer is "numbers bigger than -7"

Answer 11

ohhh so it is b?

Answer 12

to write "numbers bigger than -7"
you write -7 then you write either < or >. the "small end" of the < symbol points at the smaller number, and the "fat end" points at the bigger numbers.
-7 < x is one way
or x > -7
is another.

Answer 13

Because you have an open circle, you use > or <
if you have a solid circle, then the answer could equal -7, and you use
\( \le \) or \( \ge\)

Answer 14

but, im still confused. how do i solve it if y isnt -7?

Answer 15

It looks like they are using y for the "solutions" (not x)
also they added +5 to both sides.

Answer 16

what does it mean by "both sides"

Answer 17

First, which should we use
y > -7
or
y < -7
?

Answer 18

uhh, >?

Answer 19

but what is y?

Answer 20

in other words, how do you translate those equations into English?

y > -7 reads " numbers (given the name "y") bigger than -7
Examples: -6,-5, 0, 1, etc

Answer 21

y is a name for "numbers that are the solution"

Answer 22

none of your choices show
y > -7
but if we add +5 to both sides:
y+5 > -7 + 5
and simplify the right side

Answer 23

so its A?

Answer 24

yes

Answer 25

Ohhh ok. thanks for the help (im stupid in case you havent noticed :/)

Answer 26

Look at the number line. do you see the red arrow?
it is trying to show "numbers bigger than -7"
does that part make sense ?

Answer 27

ohhh

Answer 28

so then with this question, the choices would be either B or D right?

Answer 29

because of the arrows

Answer 30

now you have to learn how to write
"numbers bigger than -7"
using > or <

you have to write
-7
and then < (remember the "small end" of the < points at the smaller number, and -7 is the smallest number)
so

-7 <
and now give a "name" for the numbers. people use x or y (why not?). Here they use y:
-7 < y

now you have to match that to your choices.

Answer 31

For your second problem
It is tricker.

Answer 32

ruh roh...

Answer 33

\[ - \frac{s}{2} \ge 9 \]

first notice it's greater than or EQUAL, so the answer should have a solid dot (not an open circle). Unfortunately, all the choices have a solid dot.

Answer 34

isnt that good?

Answer 35

Second, you have to be careful about minus signs.
one way around the trick is to add +s/2 to both sides:
\[ - \frac{s}{2} +\frac{s}{2} \ge 9 +\frac{s}{2} \\ 0 \ge 9 +\frac{s}{2}
\]
now add -9 to both sides:
\[ 0 -9 \ge 9-9 +\frac{s}{2} \\ -9 \ge \frac{s}{2} \]

Answer 36

\[ -9 \ge \frac{s}{2} \]
to get s by itself, it's ok to multiply by a (positive) number 2:
\[ -9 \cdot 2\ge \frac{s}{2}\cdot 2 \\ -18 \ge s \]

Answer 37

once you get to this stage, you should be able to pick out the correct picture.

They used "s" for the name of the numbers in the solution.
Can you translate this to English:
\[ -18 \ge s\]

Answer 38

...

Answer 39

huuuuuh?

Answer 40

oh wait

Answer 41

B?

Answer 42

OS is a bit flaky...
but did you read the posts up above, about this problem?

Answer 43

Did you see how to change
-s/2 >= 9
to
-18 >= s

?
next, what does this mean : -18 >= s in English ?

Answer 44

ok im back

Answer 45

yes i saw how to change it

Answer 46

@phi

Answer 47

next, what does this mean : -18 >= s in English ?

Answer 48

its greater or equal to s? im still confused

Answer 49

close. -18 is bigger or equal to "all numbers we are interested in"
(s are the numbers we are interested in)

Answer 50

notice we can write it this way:
s <= -18

how do you translate that to English ?

Answer 51

s is less or equal to -18? I think the answer is B?

Answer 52

Yes,
s is less or equal to -18
and that means the same thing as
-18 is bigger or equal to s

Agree ?

Answer 53

yea

Answer 54

now think about
s is less or equal to -18

Can you name a few numbers that s could be ?

Answer 55

-20 -22 -24 etc? (can you help me with 1 more after this? i think its shorter)

Answer 56

yes. almost done with this one. which choice shows an arrow that starts at -18 and "covers" your numbers -20, -22, etc. ?

Answer 57

A

Answer 58

yes. that is the answer.

Answer 59

Coolio. Heres the last one.

Answer 60

can you get t by itself ? remember, multiplying by a negative number "switches" the >= operator.

Answer 61

what do you mean by "switch it"

Answer 62

If you look back at the previous problem
-s/2 >= 9
turned into
s/2 <= -9
I did it by adding -s/2 to both sides, then -9 to both sides)
the short way is to multiply by -1 and "switch" >= to <=

Answer 63

ohh

Answer 64

so now its t/5 <= -15?

Answer 65

minus signs are tricky: -1 < 2 (for example).
if we multiply by -1 on both sides we get -1*-1 < -1*2 which becomes
1 < -2 which is not true. The answer is "don't multiply by negative numbers"
or "if you do, switch the operator"

Answer 66

so now its t/5 <= -15?

yes. last step: multiply both sides by 5, and simplify

Answer 67

A?

Answer 68

yes
\[ 5 \cdot \frac{t}{5} \le -15 \cdot 5\\
t \le 75

\]

Answer 69

Cool. Thanks for all the help (sorry i took up alot of your time)

Answer 70

yw