Question

Solve and graph the absolute value inequality: |2x + 4| > 8.

number line with open circles on −6 and 2, shading in between.

number line with closed circles on −6 and 2, shading going in the opposite directions.

number line with open circles on −6 and 2, shading going in the opposite directions.

number line with open circles on −2 and 2, shading going in the opposite directions.

Answer 1

@ganeshie8 @dumbcow @phi

Answer 2

@Hero

Answer 3

First, does the > mean open circle or closed circle ?

Answer 4

open

Answer 5

so cross off the choice that says "closed"

that leaves 3 choices.

Answer 6

I think it's A but I'm not sure

Answer 7

how about the first choice
number line with open circles on −6 and 2, shading in between.
?

shading "in between" -6 and 2. Pick an easy number in between -6 and 2 and see if it "works"

for example, let x=0
is |2 * 0 + 4 | > 8
?

Answer 8

what is 2 times 0 ?
then add 4
what do you get

Answer 9

the answer is false,

Answer 10

2 * 0 = 0

Answer 11

0 + 4 = 4

Answer 12

4 is not bigger than 8

Answer 13

and the | 4 | means make 4 positive. i.e. you get just 4
(because 4 is already positive)

so cross off choice A.

Answer 14

C? because D does not make sense to me..

Answer 15

it's either C or D

D says -4 should work (for example)

Answer 16

if we test -4, we get

| -4 * 2 + 4 | = | -8 + 4 | = | -4 | = 4
and 4 > 8 is false.

so that leaves C

Answer 17

Okay, Thanks! can you help me with one more?

Answer 18

it is just like this one,

Answer 19

the other way is to solve for x.

we set up two relations

2x + 4 > 8
and
-(2x + 4) > 8


solve the first one:
add -4 to both sides
2x +4 - 4 > 8 -4
2x > 4
divide both sides by 2
x > 2

so x bigger than 2... shade in the numbers bigger than 2

now the 2nd relation
-(2x + 4) > 8
distribute the - sign (it means multiply by -1)
-2x - 4 > 8
add +4 to both sides
-2x -4 + 4 > 8 +4
-2x > 12

now it is trick to multiply or divide by a negative number. To stay out of trouble, I ALWAYS ADD OR SUBTRACT

add +2x to both sides.
-2x + 2x > 2x+12
0 > 2x+12

now add -12 to both sides
-12 > 2x
divide both sides by 2
-6 > x

or
x< - 6

x is smaller than -6