Key Concepts
- Inequalities are solved using the following properties.
Addition Property
Let, [latex]a,b,[/latex] and [latex]c[/latex] be real numbers.
If [latex]a
This statement also holds for [latex]a \leq b, a>b,[/latex] and [latex]a \geq b[/latex].
Multiplication Property
Let, [latex]a,b,[/latex] and [latex]c[/latex] be real numbers.
If [latex]a0[/latex] then [latex]a \cdot c
If [latex]ab \cdot c[/latex].
This statement also holds for [latex]a \leq b, a>b,[/latex] and [latex]a \geq b[/latex].
- We solve an inequality by isolating the variable, just like when solving an equation, but remember to reverse the inequality when multiplying or dividing by a negative number.
- A compound inequality involving or has a solution set made up of all real numbers which satisfy the first inequality or the second inequality, or both.
- The solution to an and compound inequality is all the solutions that the two inequalities have in common. This is where the two graphs overlap.
Glossary
compound inequality: two inequalities joined with the word and or the word or.
Candela Citations
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- Revision and Adaptation. Provided by: Lumen Learning. License: CC BY: Attribution
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- Unit 10: Solving Equations and Inequalities, from Developmental Math: An Open Program. Provided by: Monterey Institute of Technology and Education. Located at: http://nrocnetwork.org/dm-opentext. License: CC BY: Attribution