How do you solve #-x/5+12<4# and graph on the number line?

1 Answer
Tony B
Nov 15, 2016

#x>40#

Notice that the 'blob' at the left hand side of the red line on the axis is #color(red)(ul("not filled in"))#. This means that #x# does not actually take on the value of 40.

Explanation:

Multiply both sides by (-1) to make the x term positive. Note that this act turns the inequality sign the other way round.

#-x/5+12 < 4" "->" "+x/5-12 > -4#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Why does it turn the inequality round?")#

Consider #a>3#

In this instance #a# is positive and greater than 3. So for example
#4 > 3#

What happens if we multiply by (-1) but not change the sign round? We get this: #-4 > -3# Clearly this is wrong so we need to reverse the sign. Thus #(-1)(a>3)" becomes "-a< -3#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Continuing the answer")#

Add 12 to both sides giving:

#x/5 > 8#

Multiply each side by 5

#" "color(green)(ul(bar( |color(white)(./.)x>40color(white)(./.)|)))#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Tony B

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