If we divide both sides by a positive number, the inequality is preserved. You may select which type of inequality to use in the problems.
If the inequality is an "And" compound inequality, then the solution is the intersection of the solution sets for both inequalities. This is written formally as: On this number line, points B and A are our original values of 2 and 5. In 7 years, Ellie will be old enough to vote in an election.
In the next lesson, you will solve disjunction compound inequalities. Take a look with me Remember, these two examples are two different ways to solve the same problem. The Division Properties of Inequality work the same way.
Did you notice how the solution set for each individual inequality did not overlap at all? The stocks were not worth the same amount in the beginning, so if each stock loses half its value, the new values will not be equal either. So, whatever you do side 1, you must also do to sides 2 and 3.
This one inequality can be broken into 2 different inequalities: Do you notice how the solution set for the compound inequality only includes the solution sets that intersect or overlap on the graph?
We will be uniting the solution sets instead. Instead of separating this into two inequalities, we are going to leave it as one. This can also be written as: We can then use the Subtraction Property of Inequality to solve for e. Part 1 is the part of the inequality that needs to be solved for x.
We could write this inequality as: This is the most important rule to remember for "AND" compound inequalities.
The solution to a compound inequality containing the word "or" is the union of the solution sets. It would be much easier to graph if we reversed the sides with the smaller number first. If we take the same two numbers and multiply them by You may not see the word "and" in the original inequality, but when you read the inequality aloud, you will say the word "and".
This pattern holds true for all inequalities—if they are multiplied by a negative number, the inequality flips. In a sense we are uniting these two answers in order to include both.
These are the inequalities with the word "or".
For example, here is a problem where we can use the Subtraction Property to help us find a range of possible solutions: Just remember to follow the same rules as for regular inequalities, but now you are solving two inequalities within one problem.
You may select which type of inequality and the type of numbers to use in the problems. The final graph for this compound inequality would look exactly as it is shown:Solve each compound inequality.
Graph your solutions. 3. 5 y +2 > —10 —12 —10 4 5. 6b — 4 Write a compound inequality for each situation.
Graph your solution. Water will not be in liquid form when it is colder than F or warmer than F. t. Part 2: Write a compound inequality that represents each phrase. Graph the solutions.
3) All real numbers that are greater than and less than or equal to. 4) The time brownies must bake is between 15 minutes and 25 minutes. 5) All real numbers that are less than or greater than. Part 3: Solve and graph each of the compound inequalities.
COMPOUND INEQUALITIES WORKSHEET Solve each inequality and graph its solution. 1. 2 66r o xx Create a compound inequality for the following word problems. Write an inequality that represents the temperatures where sharks will NOT thrive. A summary of Compound Inequalities in 's Compound Inequalities.
Learn exactly what happened in this chapter, scene, or section of Compound Inequalities and what it means. Perfect for acing essays, tests, and quizzes, as well as for writing lesson plans. Compound Inequalities Date_____ Period____ Solve each compound inequality and graph its solution.
1) m or Solve each compound inequality and graph its solution. 1). Compound inequalities that make use of the logical “or” are solved by solutions of either inequality.
The solution set is the union of each individual solution set. Compound inequalities that make use of the logical “and” require that all inequalities are solved by a single solution.Download