I'm so confused I got the answer just don't understand how they want me to write it?

Question

Solve the inequality and express the solution set using interval notation.

4(x-8)<= -7(x + 3)

Do not convert fractions to decimal form.
Express your answer in interval notation. Inequalities will not be accepted

Answer 1

This is actually quite simple, but you have to understand interval notation. They are asking you to use parentheses ( ) and brackets [ ] instead of the inequality sign.

You would solve the problem normally as follows:

4(x-8) <= -7(x+3)
4x-32 <= -7x-21
Combine like terms...
11x <= 11
x <= 1

Now come the parentheses and brackets.

In interval notation, the answer is shown as:

(-∞, 1]

Note: ∞ = infinity

See the following web site for a good explanation of the usage.

http://id.mind.net/~zona/mmts/miscellaneousMath/intervalNotation/intervalNotation.html

Answer 2

Let's simplify.

4x - 32 <= -7x-21

11x-11<=0
11(x-1)<=0

i.e., x-1<=0
--> x<=1

This is an inequalty
As it is said "Express your answer in interval notation. Inequalities will not be accepted"

in interval notation it will
x ε (-infinity,0]

Notice the brackets... the first one indicates an open interval and the second one indicates a closed interval. i.e., 0 is inclusive.

Answer 3

4(x - 8) <= -7(x + 3)
4x - 32 <= -7x - 21
4x + 7x <= -21 + 32
11x <= 11
x <= 1

If x must be less than or equat to 1, you might say the interval is

[-infinity, 1]

where the brackets indicate inclusion of the points. I am a little fuzzy here, but follow the link below.

Answer 4

Interval notation would involve using brackets [x value, y value] and/or parenthesis (x value, y value). You use brackets for equations involving ≤ or ≥. You use parenthesis for < and >

Since the answer was x ≤ 1, I would write it like this:

(-∞, 1]

and this ∞ stands for x=infinity, which is how you would actually write it, not the word itself.

Answer 5

4x - 32 <= -7x - 21
11x <= 11
x<=1

interval notation x is a member of (negative infinity, 1 ]

there's that epsilon character that means "is a member of"

Use a round bracket on left, square bracket on right.

Answer 6

4(x - 8) <= -7(x + 3)
4x - 32 <= -7x - 21
11x <= 11
x <= 1

(-infinity,1]

Answer 7

THe answer you got should have been x<=1

This in interval notation would be

x ε (-infinity, 1]

The interval notation is explained pretty well at http://en.wikipedia.org/wiki/Interval_notation

Do read it.

Answer 8

4x-32<=-7x-21
7x+4x<=32-21
11x<=11
for x=1
11=11
for x=0
0<11

Answer 9

OMG my brain hurts!

Well as everybody else seems to have answered correctly & sensibly, I'll do the obligatory stupid answer! Good luck with the test :)

Answer 10

Everyone who said:

(-infinity, 1]

...is correct. :)