Express your answer using set notation or interval notation. Graph the solution set. 3-|x+1|<(1)

step 1 When you're solving this inequality, the first step is to isolate the absolute value. So we need

Express your answer using set notation or interval notation....

Key Concepts

Absolute Value

Absolute value represents the distance of a number from zero on the number line, disregarding its sign. In equations and inequalities, the absolute value expression tells us how far a variable is from a specific point, which is key in understanding and solving these types of problems.

Absolute Value Inequalities

Absolute value inequalities require considering the distance from a given point and usually involve splitting the inequality into cases based on the definition of absolute value. This means that an inequality like |expression| > constant translates into two separate inequalities that must be analyzed to determine the solution set.

Solving Inequalities

Solving inequalities involves isolating the relevant term—in this case, the absolute value—and using algebraic techniques to simplify and solve for the variable. A key consideration is the reversal of the inequality sign when multiplying or dividing by a negative number.

Set Notation and Interval Notation

Set notation and interval notation are formal ways to express the solution set of an equation or inequality. Set notation uses braces to denote all elements satisfying a condition, while interval notation provides a compact representation of a continuous range of numbers with clear indications of whether endpoints are included or excluded.

Graphing on the Number Line

Graphing a solution set on the number line is a visual method to represent all values that satisfy an inequality. This involves marking critical points, using open and closed circles to denote whether endpoints are included, and shading the region that represents the solution set.

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