More Math help needed!

[SaigonK]

Ok I am at it again, these are problems I need to LEARN, I do NOT want straight answers for them. I am looking for a total solution, the answer yes..but how do i get there?
Sort of a clear step by step. My answers will be in bold.

So if you want to comment I appreciate it if it is constructive, if it is not then thread crap somewhere else.



1. Ann's age differs from her sister's age by less than 6 years. Ann's sister is 39 years old. Write an absolute value inequality that describes the relationship between the ages. What are the possibilities for Ann's age? Write a complete solution.

2. Solve for x: |x - 1| = 3.

A) {2}
B) {?2}
C) {?2, 4} <---Correct answer
D) {2, ?4}


3. Choose the compound inequality that represents the graph below.


3 5

<-----------(||||||||||||||||||||||||)------------->

A) x < 3 or x < 5
B) x < 3 and x < 5
C) x > 3 and x < 5
D) x > 1 or x < 5

4. Solve the compound inequality: 3x ? 2 > 7 and 4x + 4 =< 20.

A) (3, 4]
B) (3, ?) or (??, 4] Note if you see question marks they are infinity signs that did not post correctly.
C) (??, 4]
D) (??, ?)

5. Solve the inequality. State the solution set using interval notation.
5 =< 3x+5 =< 11

6. Solve for y: 0.04y + 0.08(50 ? y) = 3.5.

A) {1.25}
B) {10}
C) {12.5}
D) {13}

7. Solve the following equation for x and check your result.
4(3x - 3) = 2(-3x + 8)

A) {3.89}
B) {1.56}
C) {-2.80}
D) {-0.31}

8. The Ricetown library carries 50 different magazines. Let L represent the number at the Lakeville library and B represent those at the Brownville library. Write an inequality showing the relationship between the three libraries if Brownville carries more than 3 times the number of magazines handled by both of the other libraries combined.

A) 3B < 50L
B) B > 3L
C) B > 3(L + 50)
D) B + L + 50 < 3

9. Solve the inequality: 0 < 1 ? 2x < 5.

A) 0 < x < 2
B) ?2 < x < 0
C) ?2 < x < 1/2
D) 1/2 < x < 2

10. Solve the inequality: 4< 7-3x <10

 

[Orsorum]

1. Ann's age differs from her sister's age by less than 6 years. Ann's sister is 39 years old. Write an absolute value inequality that describes the relationship between the ages. What are the possibilities for Ann's age? Write a complete solution.

We would take Ann's age to be "x". We don't know what x is, but we can specify a range that satifies the conditions, namely that the difference between Ann's age and her sister's is 6 or less.

Because we're writing an absolute value inequality, we only have to write one of 39-x or x-39:
|39-x|.

Their maximum difference is 6, so we can then write this as |39-x| < 6.

We can find the range of possible values by then working backwards, or considering the two cases 39-x < 6 and x-39 < 6. We get 33 < x < 45. Make sense?

 

[DaWhim]

no offensive, but is this high school math? I am just wondering, since I know I have done the math like this, but I forgot them all already.

 

[Muzzan]

4(3x - 3) = 2(-3x + 8)
12x - 12 = -6x + 16
18x - 12 = 16
18x = 28
x = 28/18 = 14/9

---------

0 < 1 - 2x < 5

Leads to equation 1:

0 < 1 - 2x
-1 < -2x
1 > 2x
2x < 1
x < 1/2

and equation 2:

1 - 2x < 5
-2x < 4
x > -2

So x must be lower than 1/2, but higher than -2:

-2 < x < 1/2

 

[FeathersMcGraw]

Absolute value is defined as |f(x)| = f(x) if f(x) >= 0, and -f(x) if f(x) < 0.

In English, it means you remove the negative sign from anything that's negative. |5| = 5, |-5| = 5. This means for systems of equations for absolute values, you will usually have to break things down into two cases. First solve the positive case as if the absolute value signs didn't exist, and second, multiply the contents of the absolute value sign by -1 (since if it's negative, multiplying by -1 makes the result positive) and solve for the negative case.

 

[SaigonK]

We would take Ann's age to be "x". We don't know what x is, but we can specify a range that satifies the conditions, namely that the difference between Ann's age and her sister's is 6 or less.

Because we're writing an absolute value inequality, we only have to write one of 39-x or x-39:
|39-x|.

Their maximum difference is 6, so we can then write this as |39-x| < 6.

We can find the range of possible values by then working backwards, or considering the two cases 39-x < 6 and x-39 < 6. We get 33 < x < 45. Make sense?

I think i got this one, but wasnt sure.

So it would be |sisters age-x (ann;s age| < (less than) 6 (years less than) correct?

 

[gopunk]

kind of surprised no one got the easy one... 3 is c

there isn't really much process to this except to know the standard notation for these things. () is exclusive, and [] is inclusive. so if i wrote (3,5], that would mean x > 3 and x <= 5.

 

[Orsorum]

Originally posted by: SaigonK

We would take Ann's age to be "x". We don't know what x is, but we can specify a range that satifies the conditions, namely that the difference between Ann's age and her sister's is 6 or less.

Because we're writing an absolute value inequality, we only have to write one of 39-x or x-39:
|39-x|.

Their maximum difference is 6, so we can then write this as |39-x| < 6.

We can find the range of possible values by then working backwards, or considering the two cases 39-x < 6 and x-39 < 6. We get 33 < x < 45. Make sense?

I think i got this one, but wasnt sure.

So it would be |sisters age-x (ann;s age| < (less than) 6 (years less than) correct?

You got it.

 

[SaigonK]

Muzzan

4(3x - 3) = 2(-3x + 8)
12x - 12 = -6x + 16
18x - 12 = 16
18x = 28
x = 28/18 = 14/9

---------

0 < 1 - 2x < 5

Leads to equation 1:

0 < 1 - 2x
-1 < -2x
1 > 2x
2x < 1
x < 1/2

and equation 2:

1 - 2x < 5
-2x < 4
x > -2

So x must be lower than 1/2, but higher than -2:

-2 < x < 1/2

I am not sure what this means....any help?

 

[SaigonK]

Quote

--------------------------------------------------------------------------------
Originally posted by: SaigonK

Quote

--------------------------------------------------------------------------------
We would take Ann's age to be "x". We don't know what x is, but we can specify a range that satifies the conditions, namely that the difference between Ann's age and her sister's is 6 or less.
Because we're writing an absolute value inequality, we only have to write one of 39-x or x-39:
|39-x|.
Their maximum difference is 6, so we can then write this as |39-x| < 6.
We can find the range of possible values by then working backwards, or considering the two cases 39-x < 6 and x-39 < 6. We get 33 < x < 45. Make sense?
--------------------------------------------------------------------------------


I think i got this one, but wasnt sure.
So it would be |sisters age-x (ann;s age| < (less than) 6 (years less than) correct?
--------------------------------------------------------------------------------

You got it.

Woohoo! 🙂

 

[Luagsch]

4. Solve the compound inequality: 3x ? 2 > 7 and 4x + 4 =< 20.

A) (3, 4]
B) (3, ?) or (??, 4] Note if you see question marks they are infinity signs that did not post correctly.
C) (??, 4]
D) (??, ?)
-------------
3x>9
x>3

4x=<16
x=<4

so answer is A)

 

[SaigonK]

gopunk

kind of surprised no one got the easy one... 3 is c

there isn't really much process to this except to know the standard notation for these things. () is exclusive, and [] is inclusive. so if i wrote (3,5], that would mean x > 3 and x <= 5.

<B>
So anything inside () is exclusive and anything inside [ ] is inclusive correct?

But how do you get the results from the graph?

</B>

 

[Luagsch]

5. Solve the inequality. State the solution set using interval notation.
5 =< 3x+5 =< 11
-------
¦-5
0=<3x=<6
¦/3
0=<x=<2
[0, 2]

EDIT what i did is after the ¦ (which affects the whole inequality)

 

[SaigonK]

Solve the compound inequality: 3x ? 2 > 7 and 4x + 4 =< 20.
A) (3, 4]
B) (3, ?) or (??, 4] Note if you see question marks they are infinity signs that did not post correctly.
C) (??, 4]
D) (??, ?)
-------------



ok so 3x-9 (because >2 7 (two greater than seven is nine)
And 4x=<16 because? becuas you subtract 4 from < 20? Which gives you your 4x=<16

Not sure about the rest....

3x>9
x>3
4x=<16
x=<4

 

[Luagsch]

6. Solve for y: 0.04y + 0.08(50 ? y) = 3.5.

A) {1.25}
B) {10}
C) {12.5}
D) {13}

¦ *100 (why not😉 it's easier to calculate)

4y+8(50-y)=350
gives you 4y+400-8y=350
simplify
400-4y=350
¦+4y
¦-350
4y=50
¦/4
y=50/4=12,5
C) {12,5}

EDIT stuff after ¦ is what i did

 

[Luagsch]

7. Solve the following equation for x and check your result.
4(3x - 3) = 2(-3x + 8)

A) {3.89}
B) {1.56}
C) {-2.80}
D) {-0.31}
---------------
simplify equation gives
12x-12=16-6x
¦+6x
¦+12
18x=28
¦/18
x=28/18=1.56
answer is B)
insert and check: yes, right

EDIT again stuff after ¦ is what i did

 

[Luagsch]

8. The Ricetown library carries 50 different magazines. Let L represent the number at the Lakeville library and B represent those at the Brownville library. Write an inequality showing the relationship between the three libraries if Brownville carries more than 3 times the number of magazines handled by both of the other libraries combined.

A) 3B < 50L
B) B > 3L
C) B > 3(L + 50)
D) B + L + 50 < 3
---------------------------
C)

Brownville > 3(Lakeville+Ricetown)

EDIT how-to: "number of magazines handled by both of the other libraries combined" this is L+50 (the 50 are in Ricetown).
"more than 3 times" so there is something like >3* the rest; so it has something like >3(L+50)
"Brownville carries blabla" so left is B from Brownville. that gives you B> 3(L+50)

 

[Luagsch]

9. Solve the inequality: 0 < 1 ? 2x < 5.

A) 0 < x < 2
B) ?2 < x < 0
C) ?2 < x < 1/2
D) 1/2 < x < 2
----------------------
0 < 1 ? 2x < 5
¦ *(-1) (remember *(-1) changes "<" to ">")
0>2x-1>-5
¦ +1
1>2x>-4
¦ /2
1/2>x>-2 now turn around tha stuff
-2<x<1/2 so C) is solution

EDIT in between steps

 

[Luagsch]

10. Solve the inequality: 4< 7-3x <10
---------------

4< 7-3x <10
¦ *(-1) (changes "<" to ">"

(if you are not sure about it, just try the example -3<-1 if you multiply with -1 and don't change the stuff around you get something wrong (3<1 which obviosly is wrong)

-4>3x-7>-10
¦+7
3>3x>-3
¦ /3
1>x>-1
x (-1, 1)

 

[Luagsch]

Originally posted by: SaigonK
Solve the compound inequality: 3x ? 2 > 7 and 4x + 4 =< 20.
A) (3, 4]
B) (3, ?) or (??, 4] Note if you see question marks they are infinity signs that did not post correctly.
C) (??, 4]
D) (??, ?)
-------------



ok so 3x-9 (because >2 7 (two greater than seven is nine)
And 4x=<16 because? becuas you subtract 4 from < 20? Which gives you your 4x=<16

Not sure about the rest....

3x>9
x>3
4x=<16
x=<4

in equasions you do the same for the left and the right side (i did a (¦*3) for example to show what i did in the other answers.

so the original was
3x ? 2 > 7 (1) and 4x + 4 =< 20 (2)
on (1) you do ¦+2 that gives you 3x>9 then a ¦/3 which gives you x>3 for (1)
on (2) you do ¦-4 that gives you 4x=<16 then a ¦/4 which gives you x=<4
so from (1) you know x > 3 from (2) you know x is =<4 so you get (3, 4]

 

[Luagsch]

ygpm

 

[TuxDave]

SaigonK, so ...I'm a lazy bastard and which one do you still need explainations for? I don't really want to start reading all the above posts.

 

[Indolent]

why does it look like everyone but saigon is doing saigon's homework?

 

[SaigonK]

why does it look like everyone but saigon is doing saigon's homework?

These are actually example problems, people are nice enough to help me out and show me how they get done. (Luagsch gave me what i was hoping for, directions, not just an answer.)