Homework 5 multi-step & compound inequalities – Embark on a mathematical journey with homework 5, where we delve into the intricacies of multi-step and compound inequalities. These mathematical tools empower us to tackle real-world problems with precision and confidence. Prepare to unravel their concepts, techniques, and practical applications, equipping yourself with the knowledge to conquer any inequality challenge.
Multi-step inequalities introduce a systematic approach to solving inequalities involving multiple operations. We’ll explore the steps involved in isolating the variable and determining the solution set. Compound inequalities, on the other hand, present a combination of inequalities connected by logical operators.
We’ll uncover the types of compound inequalities and the strategies for solving them.
Multi-Step Inequalities: Homework 5 Multi-step & Compound Inequalities
Multi-step inequalities are algebraic inequalities that require multiple steps to solve. They typically involve operations such as addition, subtraction, multiplication, and division, and may also include inequalities such as <, >, ≤, and ≥.
Solving Multi-Step Inequalities, Homework 5 multi-step & compound inequalities
- Isolate the variable term on one side of the inequality.
- Simplify the inequality by performing the necessary operations on both sides.
- Check for any potential solutions that may be excluded by the inequality symbol.
- Write the solution in interval notation.
For example, to solve the inequality 2x + 5 < 15, we would first subtract 5 from both sides to get 2x < 10. Then, we would divide both sides by 2 to get x < 5. The solution to this inequality is the interval (-∞, 5).
Compound Inequalities
Compound inequalities are algebraic inequalities that combine two or more inequalities using the words “and” or “or”. They can be classified into two types: conjunctive inequalities and disjunctive inequalities.
Conjunctive Inequalities
Conjunctive inequalities are compound inequalities that use the word “and” to connect two or more inequalities. The solution to a conjunctive inequality is the intersection of the solutions to the individual inequalities.
For example, the solution to the inequality x > 2 and x < 5 is the interval (2, 5).
Disjunctive Inequalities
Disjunctive inequalities are compound inequalities that use the word “or” to connect two or more inequalities. The solution to a disjunctive inequality is the union of the solutions to the individual inequalities.
For example, the solution to the inequality x > 2 or x < 5 is the interval (-∞, 2) ∪ (5, ∞).
Applications of Multi-Step and Compound Inequalities
Multi-step and compound inequalities have numerous applications in real-world scenarios. They can be used to solve problems in a variety of fields, including:
- Engineering
- Physics
- Economics
- Finance
- Computer science
For example, in engineering, multi-step inequalities can be used to determine the safe operating range of a machine. In economics, compound inequalities can be used to model the relationship between supply and demand.
Question & Answer Hub
What is the difference between a multi-step inequality and a compound inequality?
Multi-step inequalities involve multiple operations to solve, while compound inequalities combine two or more inequalities using logical operators.
How do I solve a multi-step inequality?
Follow the steps: isolate the variable, simplify, and check the solution.
What are the types of compound inequalities?
Conjunctive (and) and disjunctive (or) inequalities.
