How do you solve #-8x>24#?

2 Answers
smendyka
Feb 25, 2017

See the entire solution process below:

Explanation:

Divide each side of the inequality by #color(blue)(-8)# to solve for #x# while keeping the inequality balanced. However, because we are multiplying or dividing by a negative term we must reverse the inequality:

#(-8x)/color(blue)(-8) color(red)(<) 24/color(blue)(-8)#

#(color(blue)(cancel(color(black)(-8)))x)/cancel(color(blue)(-8)) color(red)(<) -3#

#x < -3#

Tony B
Feb 25, 2017

Just a slightly different approach plus demonstrating a very important fact about reversal of the inequality.

#x< -3#

Explanation:

Given:#" "-8x>24#

We wish to have the #x# value as positive so multiply both sides by #(-1)#

There is a trap in doing this: Multiply by negative 1 and you reverse the inequality.

Doing it incorrectly #-> 8x > -24color(red)(larr" this is very wrong")#
Doing it correctly #color(white)(.)->8x< -24color(green)( larr" correct way round")#

Divide both sides by 8

#8/8 x< -24/8#

But #" "8/8=1" and "24-:8=3#

#" "x < -3#

Related questions
See all questions in Inequalities with Multiplication and Division
Impact of this question
5689 views around the world
You can reuse this answer
Creative Commons License