Answer:
<u>Skills needed: Linear Inequalities</u>
Step-by-step explanation:
1) Now, we need to understand the idea of linear inequalities. Linear inequalities have usually a region of points that make up the solution. Check the images I posted for reference.
There are usually 4 symbols used for inequalities:
Important note: If it includes or , then that means the solution includes points on the line.
2) In this situation, we have two lines:
(Which is the line that is more steep + Contains BOTH points A and D) and (Which is the line that is less steep + Contains ONLY point A as part of it).
We need to make 2 inequalities so Point C is the only solution.
---> This means we cannot use and as those will include points on the line (Points a and d) as solutions.
3) So or
AND or
----> For the inequality involving the line , we have two possibilities:
The y-value is greater than twice the x-value plus one
The y-value is less than twice the x-value plus one
----> Let's use Point C to see which one it will fall under. The coordinates of point C are: <u>(3, 1)</u> --> We plug in these values for y and x
1 is the y-value, 3 is the x-value.
This means that: for Point C to be a solution
4) The same rules above apply for the next line (2 possibilities):
The y-value is greater than one-fourths the x-value plus five-halves OR
The y-value is less than one-fourths the x-value plus five-halves
---> Let's plus <u>(3, 1)</u><u> in again</u>
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This means that: for Point C to be a solution