How do you solve #-8(4x+6)< -24# and graph the solution on a number line?

2 Answers
Jul 7, 2017

Answer:

#x>(-3/4)#

Explanation:

Distribute the #-8# into #(4x+6)#.
#-32x-48<-24#

Add #-48# on both sides.
#-32x<24#

IMPORTANT: Since you're dividing both sides by a negative number (#-32#), the#<#will become a#># ---> #x>(-24/32)#

After simplifying the fraction, you will end up with #x>(-3/4)#.

How To Graph the Inequality
- Draw a number line such that it includes #-3/4#. You can count by one-fourths.
- Draw a point on #-3/4#. It should be an open (not filled) point because the inequality does not include #-3/4# as an answer; in other words, any value of x HAS to be greater than #-3/4#.
It would only be a closed point if the inequality is #x>=(-3/4)#.
- Draw a straight arrow pointing to the right that connects to the point at #-3/4#.

I hope this helps a lot! :)

Jul 7, 2017

Answer:

See explanation

Explanation:

Given: #-8(4x+6) < -24#

Two approaches the first step:

#color(brown)("Approach 1")#

Multiply both sides by (-1) to make everything positive and turn the inequality sign the other way round.

#+8(4x+6) > +24larr# the wide part of > points to #8(4x+6)#

#color(brown)("Approach 2")#

Given: #-8(4x+6) < -24#
As in the algebra shortcut method of changing sides of the = sign.

Move what is on the left of the #<# to its right and move what is on the right of < to its left. In doing so change their signs

#+24<+8(4x+6)larr# the wide part of > points to #8(4x+6)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I choose the form: #+8(4x+6) > +24#

Divide both sides by 8

#4x+6>3#

Subtract 6 from both sides

#4x > -3#

Divide both sides by 4

#x> -3/4#

Number line 'graph'. The circle is hollow indicating 'greater than'.

Suppose it had been 'greater then or equal too'. In this case the circle would be filled in.
Tony B

What is actually happening: The colored in area below #y=-24# is the feasible solution area for #(x,y)#

Tony B #x> -3/4#