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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.
Solve and graph the solution set. In addition, express the solution set using interval notation.
Sketch the graph and give the domain and range.
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.
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:
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.
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.
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