How do you solve the inequality #-3x< -6# or #x + 5<= -2# ?

1 Answer
May 18, 2017

Answer:

See explanation

Explanation:

Given:

#-3x<-6" ".............Equation(1)#
#x+5<=-2" "............Equation(2)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider "Equation(1))#

Multiply both sides by (-1) to make the #x# term positive.

This action reverses the inequality sign as well as changing the signs.:

#+3x>+6#

Divide both sides by 3

#x>6/3#

#color(green)(x>2" "................Equation(1_a))#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider "Equation(2))#

Subtract 5 from both sides

#color(green)(x<=-7" "...................Equation(2_a))#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If you were to combine these you would have

#2 < x <= -7#

Tony B