MATH SOLVE

3 months ago

Q:
# 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.

Accepted Solution

A:

Answer:"number line with open circles on negative 9 and 5, shading going in the opposite directions."Step-by-step 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>14Subtract 4 on both sides:2x >10Divide both sides by 2:x >52x+4<-14Subtract 4 on both sides:2x <-18Divide both sides by 2: x <-9So 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.