Solve each inequality and express the solution set using...

Name: Problem 57, Chapter 2: Intermediate Algebra
Uploaded: 2022-02-27T18:36:45-08:00
Duration: 2 min 57 s
Channel: Debasish Das
Description: Solve each inequality and express the solution set using interval notation. (Objective 2) -3(3 x+2)-2(4 x+1) ≥0

Key Concepts

Interval Notation

Interval notation is a concise way to represent a set of numbers between two endpoints. It uses brackets and parentheses to denote whether the endpoints are included or excluded, and is a standard method for expressing solution sets for inequalities.

Multiplying or Dividing by a Negative Number

When you multiply or divide both sides of an inequality by a negative number, the inequality sign reverses. This rule is key when isolating the variable if you encounter a negative coefficient, ensuring the correct solution set is determined.

Solving Linear Inequalities

Solving linear inequalities involves using algebraic techniques similar to those used in solving linear equations, including distributing, combining like terms, and isolating the variable. However, attention must be paid to the direction of the inequality when performing operations.

Combining Like Terms

Combining like terms involves summing coefficients of terms with the same variable to simplify expressions. This process reduces complexity and is essential for clearly isolating the variable in linear inequalities.

Distributive Property

The distributive property is a fundamental algebraic property that allows you to multiply a sum by multiplying each addend individually before adding the results. It is crucial for eliminating parentheses and simplifying expressions in both equations and inequalities.

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