How do you solve #(q - 12) 3 <5q + 2#?

1 Answer
Feb 4, 2017

Answer:

See the entire solution process below:

Explanation:

First, expand the terms on the left side of the inequality:

#(3 xx q) - (3 xx 12) < 5q + 2#

#3q - 36 < 5q + 2#

Next, add #color(red)(36)# and subtract #color(blue)(5q)# from each side of the inequality to isolate the #q# term while keeping the inequality balanced:

#3q - 36 + color(red)(36) - color(blue)(5q) < 5q + 2 + color(red)(36) - color(blue)(5q)#

#3q - color(blue)(5q) - 36 + color(red)(36) < 5q - color(blue)(5q) + 2 + color(red)(36)#

#(3 - 5)q - 0 < 0 + 38#

#-2q < 38#

Now, divide each side of the inequality by #color(blue)(-2)# to solve for #q# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative term we must also reverse the inequality term:

#(-2q)/color(blue)(-2) color(red)(>) 38/color(blue)(-2)#

#(color(blue)(cancel(color(black)(-2)))q)/cancel(color(blue)(-2)) color(red)(>) -19#

#q > -19#