Question

Solve |4x-11| < 5. You must show all work. Use complete sentences to help me PLEASE!

Answer 1

Hello, Davis. You'll be 16 soon, ya? Or has your birthday already passed?

Anyways, to solve this, first solve like any normal inequality.

4x - 11 < 5
Okay, so just solve that for me, Davis.

Answer 2

I'm 16 since the beginning of the year.
And 4x<16 so x<4?

Answer 3

My name is Ryan also. No need to call me Davis.

Answer 4

Okay, so you would take 4x - 11 < 5, and since we know 4x - 11 are absolute values, and it is less than 5, we are going to add a minus five at the end. And that's really all there is too it! Then just solve it normally.

-5 < 4x - 11 < 5

Answer 5

how in the world did you get -5 < 4x - 11 < 5?

Answer 6

one thing to keep in mind is that, when they say -> |4x-11| < 5
they really mean

+1(4x-11) < 5
AND
-1(4x-11) < 5

so, "x" takes those 2 values
or as Compassionate already suggested,
-5 < (4x-11) < 5

which is another way to write the same exact thing

Answer 7

would you distribute this?
+1(4x-11) < 5
AND
-1(4x-11) < 5

Answer 8

Basically you're solving for the original equation and it's inverse.

Answer 9

This isn't making any sense to you, is it? :)

Answer 10

yes

Answer 11

Nope, thats why I'm here. Simply, I need work and a few sentences on this test review i need to turn in today... last minute too.

Answer 12

there are like.... 2 more after this as well.

Answer 13

you distribute it, and then solve the inequality, one will give you one value for "x", the other will give you a second value for "x", and "x" takes on both values

Answer 14

hmm.... jdoe doesnt explain it as well as Compassionate does unfortunately.. lol sorry.

Answer 15

hehhe, alright

Answer 16

slope intercept is y-mx+b correct?

Answer 17

y = mx+b, yes

Answer 18

Change 3x + 2y = 10 to slope-intercept form.
So it would be 2y= -3x+10?

Answer 19

correct, and then divide both sides by "2"l, to isolate "y" on the left-hand-side

Answer 20

No problem, Ryan

You see, when we say things like |5|, what we're really saying is, "how many spaces from 0 is five?"

Well, we know that 5 is positive five spaces and negative five spaces. So the absolute of five is simply positive and negative five on a graph. (see attachment 1 for example)[Screenshot 3]

As, the absolute value if |-3| is, "how many spaces from 0 is -3? How many spaces from 0 is positive 3?" Well, it's positive and negative 3 spaces. Right?

So back to your equation, it's asking: |4x-11| < 5
You have the absolute value: |4x-11| You're basically finding the positive and negative spaces.

I'm being asked: "How many spaces to the right and left is 4x - 11 from 0?"

So we know the positive spaces is 4x-11
And the negative spaces would be: -4x + 11 (because we multiplied by -1[or just take the inverse])

that makes sense, doesn't it?
So now we're left with two inequalities. The positive one (or the original one) solves for the right side of the graph, and the negative one solves from the left side.

So you have the two inequalities: 4x - 11 < 5 and -4x + 11 < 5
Now just solve each inequality and that's your solution!

Answer 21

woah there...

Answer 22

I hope this was helpful1

Answer 23

2y= -3x+10
# divide both sides by 2
$$
2y= -3x+10\\
\cfrac{2y}{2}= -\cfrac{3x}{2}+\cfrac{10}{2}
$$

Answer 24

so x<4 and x>3/2 is my final answer?

Answer 25

and y= 3/2x+5?

Answer 26

Ryan, you're a pro at this.

Answer 27

:)

Answer 28

y= -3/2x+5 bear in mind the 3/2 is negative :)

Answer 29

y-int is b in y+mx+b correct?

Answer 30

yes

Answer 31

double checking ;)

Answer 32

y=mx+b
Subtact 3x on both sides.
2y=-3x+10
Divide by 2.
y= -3/2x +5

Slope: -3/2
y-int: 5

Answer 33

y-intercept, that is, where the function "touches" the y-axis

Answer 34

Yes! Only 1 more question left on my review!

Answer 35

i knew that part... im not that dumb. lol xD

Answer 36

Find the equation in standard form which passes through (3, –6) and (–2, –1)?

Answer 37

well, what would be the slope for that?

Answer 38

use point-slope?

Answer 39

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Answer 40

once you get the slope, first, you use the point-slope form then

Answer 41

m is the slope. dunno how to find it. but -5/5 which is -1 for the rest.

Answer 42

WAIT! Slope: m=-1! duh!

Answer 43

hehe

Answer 44

right?

Answer 45

yes, now see this example

http://www.coastal.edu/mathcenter/HelpPages/Line(Point-Slope)/img002.GIF

Answer 46

you were given 2 points, use either on the point-slope form, then solve for "y"

Answer 47

wut
dafuq
is dat....

Answer 48

hehehe

Answer 49

dammit, help?

Answer 50

sorry I got really lagged for a bit :/