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)#
