Solve each inequality, Graph the solution set and write the answer in interval notation. 9-2 w ≤

step 1 The first thing we're being asked to do in this problem is to solve the inequality. Remember, we

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

Key Concepts

Linear Inequalities

Linear inequalities are similar to linear equations but involve inequality symbols (such as <, ?, >, ?) instead of an equality sign. They can be solved by isolating the variable on one side through inverse operations such as addition, subtraction, multiplication, or division. It is important to remember that when multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality must be reversed to maintain the correct relationship.

Graphing Solution Sets on a Number Line

Graphing a solution set on a number line involves marking the value where the inequality changes and shading the region that satisfies the inequality. In cases where the inequality includes the boundary (using ? or ?), a closed circle is used to denote that the endpoint is included. For strict inequalities (< or >), an open circle is employed to indicate that the endpoint is not part of the solution.

Interval Notation

Interval notation is a concise way to express the set of solutions to an inequality. It uses brackets and parentheses to indicate whether an endpoint is included or excluded in the solution set. A bracket '[' or ']' is used to indicate that the endpoint is included, while a parenthesis '(' or ')' denotes that it is not included. This notation provides a clear and standardized method for representing continuous intervals on the number line.

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