How do you solve #-30+5x <4(6+8x)#?

1 Answer
Mar 12, 2017

Answer:

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis on the right side of the inequality by multiplying each term within the parenthesis by #color(red)(4)# - the term outside the parenthesis:

#-30 + 5x < color(red)(4)(6 + 8x)#

#-30 + 5x < (color(red)(4) xx 6) + (color(red)(4) xx 8x)#

#-30 + 5x < 24 + 32x#

Next, subtract #color(red)(5x)# and #color(blue)(24)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#-30 + 5x - color(red)(5x) - color(blue)(24) < 24 + 32x - color(red)(5x) - color(blue)(24)#

#-30 - color(blue)(24) + 5x - color(red)(5x) < 24 - color(blue)(24) + 32x - color(red)(5x)#

#-54 + 0 < 0 + (32 - 5)x#

#-54 < 27x#

Now, divide each side of the inequality by #color(red)(27)# to solve for #x# while keeping the inequality balanced:

#-54/color(red)(27) < (27x)/color(red)(27)#

#-2 < (color(red)(cancel(color(black)(27)))x)/cancel(color(red)(27))#

#-2 < x#

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

#x > -2#