Question 1086732
<font color="black" face="times" size="3"><font color=blue>Describe a situation that could be modeled with an inequality.</font>
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?"
--------------------------------------------------------------------------
<font color=blue>Write the appropriate inequality, using an appropriate variable. </font>
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 {{{2x+10 <= 100}}}. This inequality, when solved for x, will help us determine the max number of movies we can rent under these conditions. 
--------------------------------------------------------------------------
<font color=blue>Describe what the graph of this inequality would look like.</font>
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 {{{2x+10 <= 100}}} for x, you'll get {{{x <= 45}}}. 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).</font>