Explanation Method used: Graphing a Linear Inequality in Two Variables: 1. Replace the inequality symbol with an equal sign and graph the corresponding linear equation. Draw a solid line if the original inequality contains a ≥ or ≤ symbol. Draw a dashed line if the original inequality contains a > or < symbol. 2. Choose a test point from one of the half–planes. (Do not choose a point on the line.) Substitute the coordinates of the test point into inequality. 3. If a true statement results, shade the half-plane containing this test point. If a false statement results, shade the half-plane not containing this test point. Calculation: The given inequality is − 2 ≤ x < 5 . The above inequality can be written as in system of inequality as { x ≥ − 2 x < 5 . To sketch the graph of the solution set of the above system, first sketch the graph of the each inequality. Use the above method and obtain the graph of the each inequality is as follows. The graph of the inequality x ≥ − 2 and x < 5 is as follows. Step 1: Replace the inequality symbol by = and graph the linear equation: That is, replace the symbol < by = , and graph the linear equation x = − 2 and x = 5 . Use the intercepts concept to graph the line x = − 2 , Since x = − 2 is a vertical line with x -intercept − 2 , the line passes through the point ( − 2 , 0 ) . Similarly, the line x = 5 is a vertical line with x -intercept 5 , the line passes through the point ( 5 , 0 ) . Use above intercepts and draws the graph of the line x = − 2 as a solid line and x = 5 as a dashed line as shown below in Figure 1. From Figure 1, it is observed that the both lines are parallel to each other. Step 2: Choose a test point from one of the half–planes. (Do not choose a point on the line.) Substitute the coordinates of the test point into inequality. The line x = − 2 divides the x y -plane into three parts, namely the line itself and the two half-planes. The test point in one half-plane satisfy x ≤ − 2 and the test point in other half-plane satisfy x ≥ − 2 . To find half-plane to which the solution of x ≥ − 2 belongs, choose a test point ( 0 , 0 ) from either of the half-planes. Substitute 0 for x and 0 for y into the original inequality. x ≥ − 2 0 ≥ ? − 2 0 ≥ ? − 2 True statement Since, 0 greater than − 2 is true statement, thus the half-plane containing the test point ( 0 , 0 ) is part of the solution set of the inequality x ≥ − 2

4th Edition

ISBN: 9780321833655

Author: Robert F. Blitzer

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 5.5, Problem 37E

To determine

To sketch: The graph of the solution set of the inequality −2≤x<5 or indicate that the system has no solution.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.5, Problem 36E

Chapter 5.5, Problem 38E

Students have asked these similar questions

How long is a guy wire reaching from the top of a 15-foot pole to a point on the ground 9-feet from the pole? Question content area bottom Part 1 The guy wire is exactly feet long. (Type an exact answer, using radicals as needed.) Part 2 The guy wire is approximatelyfeet long. (Round to the nearest thousandth.)

Question 6 Not yet answered Marked out of 5.00 Flag question = If (4,6,-11) and (-12,-16,4), = Compute the cross product vx w k

Consider the following vector field v^-> (x,y): v^->(x,y)=2yi−xj What is the magnitude of the vector v⃗ located in point (13,9)? [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places]

Chapter 5 Solutions

College Algebra Essentials

Ch. 5.1 - Consider the system: {2x3y=42x+y=4. Determine if...Ch. 5.1 - Prob. 2CP Ch. 5.1 - Prob. 3CP Ch. 5.1 - Prob. 4CP Ch. 5.1 - Solve the system: {5x2y=410x+4y=7.Ch. 5.1 - Prob. 6CP Ch. 5.1 - Prob. 7CP Ch. 5.1 - Prob. 1CVC Ch. 5.1 - Prob. 2CVC Ch. 5.1 - Prob. 3CVC

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The graph of the solution set of the inequality − 2 ≤ x < 5 or indicate that the system has no solution.

Solution Summary: The author explains how to graph a linear inequality in two variables.

Videos

To sketch: The graph of the solution set of the inequality −2≤x<5 or indicate that the system has no solution.

Want to see the full answer?

Chapter 5 Solutions

The graph of the solution set of the inequality − 2 ≤ x &lt; 5 or indicate that the system has no solution.

Solution Summary: The author explains how to graph a linear inequality in two variables.

Videos

To sketch: The graph of the solution set of the inequality −2≤x<5 or indicate that the system has no solution.

Want to see the full answer?

Chapter 5 Solutions

The graph of the solution set of the inequality − 2 ≤ x < 5 or indicate that the system has no solution.