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 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.

What does and and/or mean in compound inequalities?

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.

How do I know if inequalities are or or and?

If it is a conjunction that uses the word and, the solution must work in both inequalities and the solution is in the overlap region of the graph. If it is a disjunction that uses the word or, the solution must work in either one of the equations.

What are the 5 steps to solving an inequality?

To solve an inequality, we can:

  1. Add the same number to both sides.
  2. Subtract the same number from both sides.
  3. Multiply both sides by the same positive number.
  4. Divide both sides by the same positive number.
  5. 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.

How do you graph inequalities in two variables?

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.

What is the difference between an and compound inequality and an OR compound inequality?

A compound inequality contains at least two inequalities that are separated by either “and” or “or”. The graph of a compound inequality with an “and” represents the intersection of the graph of the inequalities. A number is a solution to the compound inequality if the number is a solution to both inequalities.

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.