You already know that this is an or compound inequality, so the graph will not have any overlap and any possible solutions only have to satisfy one of the two inequalities (not both). There are four points of intersection at,,, and at the edge of the regions. Which graph represents the solution set of the compound inequality word. Crop a question and search for answer. Let me just use a different color. Fill in the blank: The shaded area represents the solution set of the inequalities,, and. This is why the compound inequality has no solution. 1 is not a solution because it satisfies neither inequality.
Let's consider an example where we determine an inequality of this type from a given graph and the shaded region that represents the solution set. So I have X is greater than or equal to negative one. It is important to understand the differences between these symbols, namely the significance of the line underneath a greater than or less than symbol and how it relates to the solution of an inequality and its graph on the number line. I am REALLY struggling with this concept. 3 is a solution because it satisfies both inequalities x x≥3 and x>0. An inequality has multiple solutions. In addition, we should also take the boundary of the region into account, where a solid line means equal to, while a dashed line means not equal to. Thus, the regions on the graph that contain solutions to the system of inequalities and are C and D. Finally, let's consider an example where we identify the region that represents the solutions to a system of inequalities represented by three inequalities. Before we move onto exploring inequalities and compound inequalities, it's important that you understand the key difference between an equation and an inequality. In essence, the key difference is between an equation and an inequality is: -. Is it possible to graph a no solution inequality on the number line? How do you solve and graph the compound inequality 3x > 3 or 5x < 2x - 3 ? | Socratic. Still have questions? Since the boundary on the left of the red region, at, is represented by a solid line and the boundary on the right of the red region, at, is represented by a dashed line, we have the inequalities and, which is equivalent to. Step one is simple since every example will include the word or or and.
This first constraint says that x needs to be less than 3 so this is 3 on the number line. Definition: In math, an equation is a statement that shows that two mathematical expressions are equal to each other using an "=" sign. Which graph represents the solution set of the compound inequality practice. Lets compare the two graphs again: The key difference here is that: The solution to or is examples are values that satisfy the first inequality or the second inequality. Which of the following numbers is a possible value for x? Nam lacinia pulvinar tortor nec facilisis.
For or, the shading would be above, representing all numbers greater than 5, and the line would be solid or dashed respectively, depending on whether the line is included in the region. The region that satisfies all of the inequalities will be the intersection of all the shaded regions of the individual inequalities. Not to mention the other answer choices such as: solution for inequality A, solution for inequality B, solution for both, "All x's are right", or "no solution" the answer always surprises me and the hint section is not helping. I feel like I've never struggled more with a concept than this one. If we had, we would have the same thing, except that the line at would be solid as it would itself be included in the region. Step #3: Analyze and determine the solution set. Which graph represents the solution set of the compound inequality? -5 < a - 6 < 2. Shading above means greater than, while shading below means less than the general line defined by. Are you ready to get started?
The shaded area in the graph below represents the solution areas of the compound inequality graph. Since we are looking for values that satisfy both inequalities, We can conclude that there are no solutions because there is no value for x that is both less than -2 and greater than or equal to -1. I want to put a solid circle on negative one because this is greater than or equal to and shade to the right. A filled-in circle means that it is included in the solution set. This problem has been solved! Note that his final example will demonstrate why step #1 is so important. Pellentesque dapibus efficitur laoreet. The variable is a real number here. A compound inequality with no solution (video. If there is no solution then how come there was two findings for x. The following free How to Solve Compound Inequalities step-by-step lesson guide will teach you how to create, analyze, and understand compound inequalities using an easy and effective three-step method that can be applied to any math problem involving a compound inequality or a compound inequality graph. Mary Beth would like to buy a jacket for $40. 2019 20:10, jesus319. Step #2: Graph both inequalities on the number line.