How do you solve the inequality: #-5(13x + 3) < - 2(13x - 3)#?

1 Answer
Aug 30, 2015

Answer:

#x in (-7/13, + oo)#

Explanation:

Start by dividing both sides of the inequality by #(-1)# - do not forget to change the sign of the inequality when you do this

#(-5(13x + 3))/((-1)) > (-2(13x - 3))/((-1))#

#5(13x + 3) > 2(13x - 3)#

Next, use the distributive property of multiplication to expand the two parantheses

# 5 * 13x + 5 * 3 > 2 * 13x + 2 * (-3)#

#65x + 15 > 26x - 6#

Rearrange to get the #x#-term on one side of the inequality

#65x - 26x > -6 - 15#

#39x > - 21 implies x > -21/39 = -7/13#

This means that your inequality will be true for any value of #x# that is greater than #-7/13#. The solution set for this inequality will be #x in (-7/13, + oo)#.