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

1 Answer
Jul 8, 2017

Answer:

See a solution process below:

Explanation:

First, expand the terms on each side of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:

#color(red)(-5)(13x + 3) < color(blue)(-2)(13x - 3)#

#(color(red)(-5) xx 13x) + (color(red)(-5) xx 3) < (color(blue)(-2) xx 13x) - (color(blue)(-2) xx 3)#

#-65x + (-15) < -26x - (-6)#

#-65x - 15 < -26x + 6#

Next, add #color(red)(65x)# and subtract #color(blue)(6)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#color(red)(65x) - 65x - 15 - color(blue)(6) < color(red)(65x) - 26x + 6 - color(blue)(6)#

#0 - 21 < (color(red)(65) - 26)x + 0#

#-21 < 39x#

Now, divide each side of the inequality by #color(red)(39)# to solve for #x# while keeping the inequality balanced:

#-21/color(red)(39) < (39x)/color(red)(39)#

#-(3 xx 7)/color(red)(3 xx 13) < (color(red)(cancel(color(black)(39)))x)/cancel(color(red)(39))#

#-(color(red)(cancel(color(black)(3))) xx 7)/color(red)(color(black)(cancel(color(red)(3))) xx 13) < x#

#-7/13 < x#

To state the solution in terms of #x# we can reverse or "flip" the entire inequality:

#x > -7/13#