Question

Which graph represents the solutions to the inequality |2x - 4| less than or greater to 14?

Answer 1

@sammixboo @EclipsedStar @

Answer 2

@Michele_Laino

Answer 3

is your inequality like this:
\[\Large \left| {2x - 4} \right| \leqslant 14\]

Answer 4

oops..we have to solve these 2 inequalities:
\[\begin{gathered}
\left| {2x - 4} \right| < 14 \hfill \\
\hfill \\
\left| {2x - 4} \right| > 14 \hfill \\
\end{gathered} \]

Answer 5

yes

Answer 6

let's start solving the first one

Answer 7

when 2x>4, then we can rewrite that inequality as below:
2x-4<14
can you solve it for x?

Answer 8

If I add 4 to both sides, I get:
2x<18

Answer 9

so x = 18?

Answer 10

we have to divide by 2 first, so we get:
x<9

Answer 11

oh okk

Answer 12

now, if 2x<4, then we can rewrite that first inequality, as below:
-2x+4<14

Answer 13

okay and then?

Answer 14

we have to subtract 4 from both sides, so we get:
-2x<10

Answer 15

alright so then what?

Answer 16

we have to divide by -2, both sides, now when we divide both sides of an inequality, by a negative number, the sense of that inequality will reverse, so we get:
x>-5

Answer 17

So its A?

Answer 18

no, since what we have found is the solution to the first inequality, namely:
\[\left| {2x - 4} \right| < 14\]
nevertheless we have to solve the second inequality yet

Answer 19

So, the solution of our first inequality, is:
-5<x<9
now the second inequality is:
\[\left| {2x - 4} \right| > 14\]

Answer 20

okay, add 4 to both sides?

Answer 21

If 2x>4, then we can rewrite that inequality, as follows:
2x-4>14
now you can add 4 to both sides, what do you get?

Answer 22

4x > 18

Answer 23

2x>18

Answer 24

now please divide both sides by 2, what do you get?

Answer 25

x > 9

Answer 26

@AllyBearxx

Answer 27

yes?

Answer 28

that's right!

Answer 29

now, if 2x<4, then we can rewrite that second inequality, as follows:
-2x+4>14