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Notes
Questions
Solve and graph
\(\textbf{1)}\) \(-4\lt4x+6\le18 \)
\(\textbf{2)}\) \(5x-4\lt34 \) and \( -5x-8\le-8\)
\(\textbf{3)}\) \(3\lt 6-2x \le18 \)
\(\textbf{4)}\) \(4x-5\lt 35 \) and \( 4-x\le-10 \)
\(\textbf{5)}\) \(x+3\gt8 \) or \( 2x\lt 16 \)
See Related Pages\(\)
\(\bullet\text{ Compound Inequality Calculator}\)
\(\,\,\,\,\,\,\,\,\text{(Symbolab.com)}\)
\(\bullet\text{ Solving Inequalities Addition and Subtraction}\)
\(\,\,\,\,\,\,\,\,4+x\ge12…\)
\(\bullet\text{ Solving Inequalities Multiplication and Division}\)
\(\,\,\,\,\,\,\,\,4x\lt 16…\)
\(\bullet\text{ Solving Multi-step Inequalities}\)
\(\,\,\,\,\,\,\,\,18-4x \lt 2…\)
\(\bullet\text{ Andymath Homepage}\)
In Summary
A compound inequality is a mathematical statement that combines two inequalities. They may use the words “and” or “or”. For example, the statement \(x \gt 2\) and \(x \lt 6\) is a compound inequality that represents the set of all values of x that are greater than 2 and less than 6. It may also be expressed as \(2 \lt x \lt 6\).
To solve a compound inequality, you solve the two separate inequalities, and then combine them. The solution to a compound inequality with the word “and” is the intersection (meaning BOTH inequalities must be true) of the solutions to the individual inequalities, while the solution to a compound inequality with the word “or” is the union (meaning EITHER of the inequalities must be true) of the solutions to the individual inequalities.
About Andymath.com
Andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. If you have any requests for additional content, please contact Andy at tutoring@andymath.com. He will promptly add the content.
Topics cover Elementary Math, Middle School, Algebra, Geometry, Algebra 2/Pre-calculus/Trig, Calculus and Probability/Statistics. In the future, I hope to add Physics and Linear Algebra content.
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