Question

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

number line with open circles on negative 9 and 5, shading going in the opposite directions.
number line with open circles on negative 9 and 5, shading in between.
number line with closed circles on negative 9 and 5, shading going in the opposite directions.
a number line with open circles on negative 5 and 5, shading going in the opposite directions.

Answer 1

"number line with open circles on negative 9 and 5, shading going in the opposite directions."

Explanation:

Your inequality doesn't include an equal sign so there will be no closed holes. It will only be open holes.

|u|>14 means that the number u has to be greater than 14 or less than -14. These numbers I describe just now all have a distance greater than 14 from 0.

So |u|>14 implies u>14 or u<-14.

But we are solving |2x+4|>14 so this implies we have 2x+4>14 or 2x+4<-14.

2x+4>14

Subtract 4 on both sides:

2x >10

Divide both sides by 2:

x >5

2x+4<-14

Subtract 4 on both sides:

2x <-18

Divide both sides by 2:

x <-9

So our solution is x>5 or x<-9.

Graphing!

~~~~~~~O O~~~~~~~~

-----------(-9)---------------------------------(5)---------------

So we shaded to the right of 5 because our inequality says x is bigger than 5.

We shaded to the left of -9 because our inequality says x is less than -9.