Question

I7x-8I less than 4. express using interval notation

Answer 1

|a|<b can be written as -b < a < b.
So in your case,

|7x - 8| < 4 is written as
-4 < 7x - 8 < 4

Add an 8 throughout, and then divide by 7.

To put in interval notation, remember that

a < x < b is written as (a,b)

Answer 2

how should that look? i dont know if i did it right

Answer 3

?

Answer 4

I'll do the first step to get you started :)

-4 < 7x - 8 < 4
4 < 7x < 12

Now what would the next line look like when you divide through by 7?

Answer 5

4/7 less than x less than 12/7?

Answer 6

right!

now for the interval notation...
if you have a < x < b, your interval notation looks like (a,b) meaning all values between a and b.

you have 4/7 < x < 12/7, so the interval notation would be...

Answer 7

(4/7,12/7)

Answer 8

?

Answer 9

perfect! :)

Answer 10

could u help with my other ? too

Answer 11

sorry...had to take a phone call.

what's the question?

Answer 12

(4/x)-(40/x+6)+3=0. find all real solutions

Answer 13

just like adding and subtracting regular fractions, you need a common denominator.

the denominators of the three fractions you have are x, x+6, and 1

Answer 14

one way to always find a common denominator is to multiply them together. you can do this with regular fractions too, but it often gives you a bigger number than you need.

in this case, however, it's all we can do.

so, your common denominator is x(x+6). don't bother multiplying it out...it's nicer in this form for now

Answer 15

your first fraction's denominator is missing the x+6, so we multiply top and bottom by it.

likewise, the second fraction is missing the x.

the thrid fraction is missing both x and x+6, so we multiply top and bottom by the whole thing.

this gives us:

4(x+6) 40x 3x(x+6)
--------- - ------ + -------- = 0
x(x+6) x(x+6) x(x+6)

Answer 16

Just like with regular fractions, once you have a common denominator, you can add the numerators and put that over the common denominator.

Answer 17

you can multiply out the individual numerators here, but leave the denominator as is for now.

4x + 24 - 40x + 3x^2 + 18x
-------------------------- = 0
x(x+6)

Answer 18

A fraction will be 0 only when the numerator is 0, so to solve this, it must be that

\[4x+24-40x+3x^{2}+18=0\]simplify the equation\[3x^{2}-36x+42=0\]

Answer 19

since every term has a 3 in it, divide through by 3.\[x^{2}-12x+14=0\]

Answer 20

have you learned how to solve quadratic equations? try to see what you get.