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Showing posts with label inequalities. Show all posts
Showing posts with label inequalities. Show all posts
Intermediate Algebra Exam #1
Click on the 10 question exam covering topics in chapters 1 and 2. Give yourself one hour to try all of the problems and then come back and check your answers.






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Chapter 2 Sample Test Questions
Click here for a worksheet containing 20 sample test questions with answers.
Odd Integer Problem: Find three consecutive odd integers whose sum is 51. (Set up an algebraic equation then solve it.)
Perimeter Problem: The perimeter of a rectangle is 110 feet. Find the dimensions if the length is 5 feet less than twice the width.
Perimeter Problem: The perimeter of a rectangle is 110 feet. Find the dimensions if the length is 5 feet less than twice the width.
Linear Inequalities (Two Variables)
When graphing an equation like y = 3x − 6 we know that it will be a line. The graph of a linear inequality such as y >= 3x − 6, on the other hand, gives us a region of ordered pair solutions.
Not only do the points on the line satisfy this linear inequality - so does any point in the region that we have shaded. This line is the boundary that separates the plane into two halves - one containing all the solutions and one that does not. Therefore, from the above graph, both (0, 0) and (−2, 4) should solve the inequality.
Graph the solution set.
If the test point yields a true statement shade the region that contains it. If the test point yields a false statement shade the opposite side.
When graphing strict inequalities, inequalities without the equal, the points on the line will not satisfy the inequality; hence, we will use a dotted line to indicate this. Otherwise, the steps are the same.
Graph the solution set.
Given the graph determine the missing inequality.
Video Examples on YouTube:





Not only do the points on the line satisfy this linear inequality - so does any point in the region that we have shaded. This line is the boundary that separates the plane into two halves - one containing all the solutions and one that does not. Therefore, from the above graph, both (0, 0) and (−2, 4) should solve the inequality.
Use a test point not on the boundary to determine which side of the line to shade when graphing solutions to a linear inequality. Usually the origin is the easiest point to test as long as it is not a point on the boundary.
Instructional Video: Linear Inequalities in Two Variables
Graph the solution set.
If the test point yields a true statement shade the region that contains it. If the test point yields a false statement shade the opposite side.
When graphing strict inequalities, inequalities without the equal, the points on the line will not satisfy the inequality; hence, we will use a dotted line to indicate this. Otherwise, the steps are the same.
Graph the solution set.
Given the graph determine the missing inequality.
Video Examples on YouTube:






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