How do you solve and graph #2(-3m - 5) ≥ -28 #?

1 Answer
Apr 2, 2017

Answer:

#m<=3#

Explanation:

Manipulate the inequality as you would an equation. However there is a trap when doing so. If you multiply by negative one then you turn the inequality round the other way. I will show you why in the explanation.

Given:#" "2(-3m-5)>=-28" ".............Equation(1)#

Divide both sides by 2 (gets rid of the 2 on the left)

#-3m-5>= -14#

Add 5 to both sides (gets rid of the 5 on the left)

#-3m>= -9#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Method 1:

#-3m>= -9#

Multiply both sides by (-1)

#color(magenta)(+3m<=+9)" ".....Equation(2)#
......................................................................
Method 2:

#-3m>= -9#

Add #3m# to both sides

#0 >=3m-9#

Add 9 to both sides

#+9>=+3m#

Write as:

#color(magenta)(3m<=+9)" "............Equation(3)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Notice that both #Equation(2) and Equation(3)# are the same
This demonstrates why you turn the inequality round the other way when you multiply by negative one

#3m<=9#

Divide both sides by 3

#m<=3#