How do you solve and graph compound inequalities?
To solve a compound inequality, first separate it into two inequalities. Determine whether the answer should be a union of sets (“or”) or an intersection of sets (“and”). Then, solve both inequalities and graph.
What is a compound inequality and how is it solved?
A compound inequality is made up of two inequalities connected by the word “and” or the word “or.” To solve a compound inequality means to find all values of the variable that make the compound inequality a true statement. We solve compound inequalities using the same techniques we used to solve linear inequalities.
What is the difference between a simple inequality and a compound inequality?
A compound inequality, sometimes referred to as combined inequality, is an inequality that combines two or more simple inequalities joined together with or or and. To be a solution of an or inequality, a value has to make only one part of the inequality true.
How do you graph an inequality?
There are three steps:
- Rearrange the equation so “y” is on the left and everything else on the right.
- Plot the “y=” line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)
- Shade above the line for a “greater than” (y> or y≥) or below the line for a “less than” (y< or y≤).
What is a compound inequality examples?
Compound inequalities are the derived form of inequalities, which are very useful in mathematics whenever dealing with a range of possible values. For example, after solving a particular linear inequality, you get two solutions, x > 3 and x < 12. You can read it as “3 is less than x, which is less than 12.
How do you know if a compound inequality is and or OR?
A compound inequality (or combined inequality ) is two or more inequalities joined together with or or and . To be a solution of an or inequality, a value has to make only one part of the inequality true. To be a solution of an and inequality, it must make both parts true. (In other words, x≥−1 and x<2 .)
When solving compound inequalities What is the difference between and and OR?
The key difference is with “or”, x only needs to satisfy one of the inequalities. With “and”, x needs to satisfy both.
What is the first step in graphing the solution set of an inequality?
To graph the solution set of an inequality with two variables, first graph the boundary with a dashed or solid line depending on the inequality. If given a strict inequality, use a dashed line for the boundary. If given an inclusive inequality, use a solid line. Next, choose a test point not on the boundary.
How do you graph the inequality?
How to Graph a Linear Inequality
- Rearrange the equation so “y” is on the left and everything else on the right.
- Plot the “y=” line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)
- Shade above the line for a “greater than” (y> or y≥) or below the line for a “less than” (y< or y≤).
What is a simple inequality?
Inequality shows relation between two objects or values. For example 3 is greater than 2, 1 is lesser than 5, 5 is equal to 5. Those are simple, well known inequalities.
What is a simple compound inequality?
A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.” “And” indicates that both statements of the compound sentence are true at the same time. It is the overlap or intersection of the solution sets for the individual statements.
What are the 5 steps to solving an inequality?
To solve an inequality, we can:
- Add the same number to both sides.
- Subtract the same number from both sides.
- Multiply both sides by the same positive number.
- Divide both sides by the same positive number.
- Multiply both sides by the same negative number and reverse the sign.
What are 3 ways to solve inequalities?
Summary. Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. But these things will change direction of the inequality: Multiplying or dividing both sides by a negative number.
What does a compound inequality look like?