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

step 1 thing we're being asked to do in this problem is to solve the given inequality. Well, you solve

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

Key Concepts

Linear Inequalities

A linear inequality is similar to a linear equation but uses inequality signs (such as <, >, ?, or ?) instead of an equals sign. The process of solving linear inequalities involves isolating the variable in a manner similar to equations, keeping in mind that multiplying or dividing both sides of an inequality by a negative number requires reversing the inequality sign.

Graphing Inequalities on a Number Line

Graphing inequalities on a number line involves representing the solution set visually by marking critical points and shading the region where the inequality holds. Open circles are typically used for strict inequalities (like < or >) to indicate that endpoints are not included, while closed circles represent inclusive inequalities (like ? or ?).

Set Notation

Set notation is a method of specifying a collection of objects, in this case, the values that satisfy an inequality. It is often written in the form {x ? ? : condition}, where the condition describes the relationship or property that the elements of the set must satisfy.

Interval Notation

Interval notation is a concise way to represent a range of numbers that satisfy an inequality. Parentheses indicate endpoints that are not included in the interval (as in the case of strict inequalities), while brackets indicate that an endpoint is included. This notation is especially useful for indicating continuous sets of real numbers.

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