Solve and graph the absolute value inequality: |2x + 4| 14?

Question

Solve and graph the absolute value inequality: |2x + 4| > 14?

jim_thompson5910 · Answer

Rule: |x| > k breaks into these two inequalities: x > k or x < -k

where k is some positive number

jim_thompson5910 · Answer

using that rule

|2x + 4| > 14

will turn into

2x + 4 > 14  or  2x + 4 < -14

jim_thompson5910 · Answer

what do you get when you solve 2x + 4 > 14  ?

anonymous · Answer

where does k come from?

jim_thompson5910 · Answer

k is just some constant

it's a placeholder for some positive number (any positive number)

anonymous · Answer

6x>14 ?

jim_thompson5910 · Answer

examples: |x| > 3 turns into x > 3 or x < -3 |x| > 12 turns into x > 12 or x < -12 etc etc

jim_thompson5910 · Answer

2x +4 doesn't turn into 6x

anonymous · Answer

Oh okay

jim_thompson5910 · Answer

2x and 4 are not common terms. You cannot add them like that

anonymous · Answer

so only add like terms

jim_thompson5910 · Answer

yes like 2x and 3x

2x+3x = 5x

jim_thompson5910 · Answer

how would you isolate x in 2x + 4 > 14

anonymous · Answer

Oh okay I see

anonymous · Answer

by getting 4 on the other side

jim_thompson5910 · Answer

how do you do that? what must you do to both sides?

anonymous · Answer

subtract 4

jim_thompson5910 · Answer

yes

anonymous · Answer

so 2x>10

jim_thompson5910 · Answer

correct

jim_thompson5910 · Answer

what's next?

anonymous · Answer

divide 2 on each side?

jim_thompson5910 · Answer

correct, giving you what?

anonymous · Answer

x>5?

jim_thompson5910 · Answer

very good

jim_thompson5910 · Answer

so 2x + 4 > 14 leads to x > 5

jim_thompson5910 · Answer

solve 2x + 4 < -14 for x

anonymous · Answer

Yes, so isnt there another equation

jim_thompson5910 · Answer

there is

jim_thompson5910 · Answer

inequality actually 

not equation

anonymous · Answer

Ok 2x+4<-14 
then subtract four from each side giving me 
2x<-18 
then divide 2 on each side leaving me with 
x<-9 ??

jim_thompson5910 · Answer

the steps and answer are correct

jim_thompson5910 · Answer

|2x + 4| > 14 will turn into 2x + 4 > 14 or 2x + 4 < -14 ----------------------- solve 2x+4 > 14 for x to get x > 5 solve 2x+4 < -14 for x to get x < -9

anonymous · Answer

so then i have to put it on  a number line graph

jim_thompson5910 · Answer

that means |2x + 4| > 14 has the solution set of x > 5 or x < -9

anonymous · Answer

Oh okay, but is < and > a closed or open circle?

jim_thompson5910 · Answer

draw out a number line

make sure +5 and -9 are on it

place open circles at +5 and -9

to graph x > 5, you'll shade to the right of the open circle at +5
to graph x < -9, you'll shade to the left of the open circle at -9

jim_thompson5910 · Answer

< or > means open circle

$\Large \le$ or $\Large \ge$ means closed circle

anonymous · Answer

Oh okay, I understand now. thank you so much!!

jim_thompson5910 · Answer

I'm glad it's making sense