Question 1086732: Describe a situation that could be modeled with an inequality. Write the appropriate inequality, using an appropriate variable. Describe what the graph of this inequality would look like. pls help
Found 2 solutions by jim_thompson5910, KMST:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Describe a situation that could be modeled with an inequality.
Often you'll be dealing with money problems where you'll want to know the total cost and you'll want to keep costs under a certain limit (i.e. stick to the budget). For instance, let's say you are part of a movie club where it costs $10 per month just to be a member. With that membership you can rent movies for $2 per movie (in contrast to $5 per movie without a membership). The question may come up: "how many movies can I rent if I have a budget of $100 for a given month?"
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Write the appropriate inequality, using an appropriate variable.
To answer the question posed above, let's make x = number of movies rented
If it costs $2 per movie, then renting x of them costs you 2*x dollars so far. This is the variable cost as it varies depending on what x is.
On top of this variable cost is the fixed cost of $10 per month to have a membership. In total, the full cost is 2*x+10 dollars
If C = 2*x+10 is that cost, and we want to keep the cost at most to $100, then we can say  . This inequality, when solved for x, will help us determine the max number of movies we can rent under these conditions.
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Describe what the graph of this inequality would look like.
The inequality in the last part has one variable. Because it has one variable, it makes the most sense to graph this on a number line. When you solve for x, you'll get  . So you graph a closed circle at 45 and shade to the left. The shaded region represents the set of x values of the solution set. In other words, it's the possible number of movies you can rent. Keep in mind that x must be a positive whole number. So the smallest x can be is x = 0. The largest x can be is x = 45. The value of x can be anything in between those endpoints as long as it's a whole number (eg: x = 27).
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! 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
 ,
where  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
 ,
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
 ,
where  = Mary's age,
and  = Mary"s brother's age.
This inequality involves two variables,
so it requires a 2-dimensional graph, like this:
 .
In this case the dashed red line means that the points on it,
like (3,3), where  and  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  ,
calling = price in $ for one can of peas,
 would be the cost of 4 cans of peas,
and  describes your situation.
If you need to be at least 40 inches tall to ride a roller coaster,
 ,
where  = your height in inches, describes that situation.
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