Solve each inequality. Graph the solution set and write the answer in a) set notation and b) int

step 1 All right. So for this problem, we are going to multiply by the reciprocal. Whenever you have a

Solve each inequality. Graph the solution set and write the...

Key Concepts

Graphical Representation on a Number Line

The solution to an inequality can be depicted on a number line where the variable's values that satisfy the inequality are highlighted. For strict inequalities (using < or >), an open circle is used to indicate that the endpoint is not included, whereas closed circles are used for inclusive inequalities (? or ?).

Set Notation and Interval Notation

Set notation and interval notation provide concise ways to express the solution set of an inequality. Set notation describes the collection of all numbers that satisfy the inequality condition, while interval notation uses parentheses and brackets to denote ranges of numbers, clearly indicating whether endpoints are included or excluded.

Linear Inequalities

This concept involves expressions where a variable is related to a constant with inequality symbols (such as <, >, ?, ?) instead of an equality sign. The goal is to isolate the variable, similar to solving equations, though extra care is needed when multiplying or dividing by negative numbers because the inequality sign reverses in that case.

Operations on Inequalities

Solving inequalities requires performing arithmetic operations on both sides while preserving the relationship. Multiplying or dividing by a positive number maintains the direction of the inequality, whereas doing so with a negative number reverses it. This principle is essential to obtain the correct solution set.

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