How do you solve and graph the compound inequality #3x > 3# or #5x < 2x - 3# ?

1 Answer
Jul 23, 2018

Answer:

#" "#
Solution:

#color(red)[(x>1) or (x < -1)#

Interval Notation:

#color(red)((-oo, -1) uu (1,oo)#

Explanation:

#" "#
We are given the inequality expression:

#color(blue)(3x > 3 or 5x < 2x - 3#

Since the #color(red)(Or# operator is used, we will use #color(red)(uu# in our final solution.

Solve the inequality expressions separately:

#color(blue)(3x>3#

Divide both the sides of the inequity by #color(red)(3#

#(3x)/3>3/3#

#(cancel 3x)/cancel 3>3/3#

#color(blue)(x > 1# ... Res.1

#color(blue)(5x < 2x - 3#

Subtract #color(red)(2x# from both sides of the inequality.

#5x-2x < 2x - 3-2x#

#5x-2x < cancel (2x) - 3-cancel(2x)#

#3x<-3#

Divide both sides of the inequality by #color(red)(3#

#(3x)/3<-3/3#

#(cancel 3x)/cancel 3<-3/3#

#color(blue)(x<-1# ... Res.2

Hence, the final solutions:

#color(red)[(x>1) or (x < -1)#

Interval Notation:

#color(red)((-oo, -1) uu (1,oo)#

Represent the solution on a graph:

enter image source here

Dotted Lines on the graph indicate values that are NOT part of the Solution Set.

Hope it helps.