In Exercises 1-8, solve the inequality algebraically. Write the solution in interval notation an

step 1 In this question here we need to solve the inequality each frequently and then we need to write

In Exercises 1-8, solve the inequality algebraically. Write...

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Key Concepts

Absolute Value

Absolute value represents the non-negative distance of a number from zero on the number line. Understanding absolute value is crucial for interpreting inequalities that measure the magnitude of an expression without regard to its sign.

Absolute Value Inequalities

Absolute value inequalities involve expressions where the absolute value of a term is compared to a number. The solution approach typically requires considering two separate cases: one where the expression inside the absolute value is greater than or equal to the given number, and one where it is less than or equal to the negative of that number, to account for both sides of zero.

Interval Notation

Interval notation is a concise way to represent the set of solutions to an inequality. It uses brackets and parentheses to denote whether endpoints are included or excluded, providing a clear and standardized method to express ranges of numbers.

Number Line Representation

A number line graphically illustrates the solution set of an inequality by marking the relevant portions of the number line. It provides a visual representation that complements interval notation, making it easier to understand the distribution of solutions.

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