Question

PLEASE HELP!!!!
Which graph represents the solutions to the inequality |2x - 6| less than or greater to 10?

number line with a closed circle on negative 2, shading to the right and a closed circle on 8, shading to the left
number line with a closed circle on negative 2, shading to the left and a closed circle on 8, shading to the right
number line with an open circle on negative 2, shading to the right and an open circle on 8, shading to the left
number line with an open circle on negative 2, shading to the left and an open circle on 8, shading to the right

Answer 1

@jdoe0001

Answer 2

@johnweldon1993

Answer 3

@kropot72

Answer 4

need help on 7 QUESTIONS
pleaseeeeeeeeeeeee

Answer 5

@roz_mar23

Answer 6

Which inequality symbol is it? You wrote less than or greater to -- do you mean less than or equal to?
\[\left| 2x-6 \right|\le10\]
Is that the original problem?

Answer 7

yup

Answer 8

@jwhite12

Answer 9

So since it's an absolute value inequality with a less than sign, you need to set up a 3-section (and) inequality without the absolute value bars, like this:
\[-10\le2x-6\le10\]

Do you know how to solve that?

Answer 10

not really no.
i also need help on some more

Answer 11

To solve a 3-section inequality, you basically solve the middle section (to get x by itself in the middle). Any steps you need to take to get x by itself, you have to do to all 3 section (left, middle, right).
So to get the x by itself in 2x-6, first we need to get rid of the 6. Do you know how to cancel or undo "minus 6"?

Answer 12

you minus it on the other side correct
like 2x/-6

Answer 13

You have to do the opposite (or inverse) of minus, which is add. So you need to ADD 6 to all 3 sections.
\[-10\le2x-6\le10\]
+6 +6 +6

This will cancel the 6's in the middle section, and leave you with:
\[-4\le2x \le16\]

Now we have 2x in the middle section. How do we cancel the 2?

Answer 14

same way

Answer 15

Nope, because 2x means "2 times x" -- this is multiplication. How do you "undo" multiplication?

Answer 16

dividing,

Answer 17

Yes! So divide each section by 2, and what do you get?

Answer 18

2 1 8

Answer 19

Be careful with your signs. -4/2 = -2

\[-2\le x \le8\]
That's the final answer. Do you know how to graph that?

Answer 20

uhmmmmm no

Answer 21

is it a

Answer 22

Ok, you make dots on the two numbers: -2 and 8.
The type of dot (open or closed) depends on whether or not the inequality symbol is "or equal to" or not. If it is "or equal to" then you make closed dots, because it includes those numbers in the solution.
So since the inequality symbol here is \[ \le \] we use closed dots on -2 and 8.

Then you shade the space in between those numbers, since our solution had x in between -2 and 8.

Answer 23

is it A