How do you solve and write the following in interval notation: #2x - 3<5# or # 3x - 2 >13#?

1 Answer
Aug 5, 2017

Answer:

See a solution process below:

Explanation:

Inequality 1:
Start to solve this inequality by adding #color(red)(3)# to each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#2x - 3 + color(red)(3) < 5 + color(red)(3)#

#2x - 0 < 8#

#2x < 8#

Now, divide each side of the inequality by #color(red)(2)# to solve for #x# while keeping the inequality balanced:

#(2x)/color(red)(2) < 8/color(red)(2)#

#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) < 4#

#x < 4#

Inequality 2
Start to solve this inequality by adding #color(red)(2)# to each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#3x - 2 + color(red)(2) > 13 + color(red)(2)#

#3x - 0 > 15#

#3x > 15#

Now, divide each side of the inequality by #color(red)(3)# to solve for #x# while keeping the inequality balanced:

#(3x)/color(red)(3) > 15/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) > 5#

#x > 5#

**The solution is: #x < 4# and #x > 5#

Or, in interval notation:

#(-oo, 4)# and #(5, +oo)#