How do you solve #2x + 24 \leq - 8x - 6#?

1 Answer
May 22, 2017

See a solution process below:

Explanation:

First, subtract #color(red)(24)# and add #color(blue)(8x)# to each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#color(blue)(8x) + 2x + 24 - color(red)(24) <= color(blue)(8x) - 8x - 6 - color(red)(24)#

#(color(blue)(8) + 2)x + 0 <= 0 - 30#

#10x <= -30#

Now, divide each side of the inequality by #color(red)(10)# to solve for #x# while keeping the inequality balanced:

#10x/color(red)(10) <= -30/color(red)(10)#

#color(red)(cancel(color(black)(10)))x/cancel(color(red)(10)) <= -3#

#x <= -3#