Question

Solve: |5x + 2| + 7 < 19
A. x < 2 and x > -14/5
B. x < 2 and x < -14/5
C. x > 2 and x > 14/5
D. x > 2

Answer 1

@nguyen8ki

Answer 2

the first thing you want to do is that you want to get rid of the absolute value sign
this leads to 2 cases:
|5x+2| = 5x+2 if x>-2/5 or
|5x+2| = -(5x+2) if x<-2/5
then we have a system of two equations:
5x+2+7<19 if x>-2/5 or -(5x+2)+7<19 if x<-2/5
5x+9 <19 -5x+5 <19
-9 -9 -5 -5
_____________________________________________________
5x < 10 or -5x <14
x < 2 and (x>-2/5) or x >-14/5 and (x<-2/5)
-2/5<x<2 or -14/5<x<-2/5
combine the two conditions we have the final answer
-14/5<x<2 so A
PS: it is a little complicated when you look at the signs and combine the conditions, the key words here are " and" and " or". these two words make the difference.