Question 1086732
An inequality describes a situation where you have or you can have, or you need
at least as much as ...,
more than ...,
no more than ...,
less than...
some number.
 
ONE EXAMPLE:
If you can hold your breath underwater for no more than 40 seconds,
the situation can be modeled by the inequality
{{{s<=40}}} ,
where {{{s}}} is the number of seconds you can hold your breath underwater.
The graph for that inequality would be a number line with the part representing the solution marked somehow.
Some teachers would tell you to color the solution on the line, like this
{{{drawing(500,100,-1,4,-0.5,0.5,
arrow(1,0,-1,0),arrow(2,0,4,0),
line(0,0.1,0,-0.1),line(1,0.1,1,-0.1),
line(2,0.1,2,-0.1),line(3,0.1,3,-0.1),
line(0.5,0.1,0.5,-0.1),line(-0.5,0.1,-0.5,-0.1),
line(1.5,0.1,1.5,-0.1),line(2.5,0.1,02.5,-0.1),
line(3.5,0.1,3.5,-0.1),locate(-0.6,-0.1,-10),
locate(-0.05,-0.1,0),locate(0.4,-0.1,10),
locate(0.9,-0.1,20),locate(1.4,-0.1,30),
locate(1.9,-0.1,40),locate(2.4,-0.1,50),
locate(2.9,-0.1,50),locate(3.4,-0.1,70),
red(line(-1,0,2,0)),red(arrow(1,0,-1,0)),
red(circle(2,0,0.05)),red(circle(2,0,0.03))
)}}} ,
meaning that 40 (under the red circle), and all the numbers to the left are solutions of the inequality.
 
ANOTHER EXAMPLE:
If Mary is older than her brother, that situation is described by the inequality
{{{x>y}}} ,
where {{{x}}}= Mary's age,
and {{{y}}}= Mary"s brother's age.
This inequality involves two variables,
so it requires a 2-dimensional graph, like this:
{{{drawing(300,300,-1,9,-1,9,
graph(300,300,-1,9,-1,9,x>y+0.12),
grid(0),red(line(0,0,0.5,0.5)),
red(line(-1,-1,-0.5,-0.5)),
red(line(1,1,1.5,1.5)),
red(line(2,2,2.5,2.5)),
red(line(3,3,3.5,3.5)),
red(line(4,4,4.5,4.5)),
red(line(5,5,5.5,5.5)),
red(line(6,6,6.5,6.5)),
red(line(7,7,7.5,7.5)),
red(line(8,8,8.5,8.5)) )}}} .
In this case the dashed red line means that the points on it,
like (3,3), where {{{x=3}}} and {{{y=3}}} are not part of the solution,
but all the point to one side of the line are part of the solution.
It could be that Mary and her brother are three-year old twins,
but Mary is a few seconds older than her brother.
 
More examples:
If you need to buy 4 cans of peas, and only have {{{$3}}},
calling {{{x}}}= price in $ for one can of peas,
{{{4x}}} would be the cost of 4 cans of peas,
and {{{4x<=3}}} describes your situation.
If you need to be at least 40 inches tall to ride a roller coaster,
{{{h>=40}}} ,
where {{{h}}}= your height in inches, describes that situation.