Solve inequality. Write the solution set in interval notation, and graph it. 6 t+3<3 t+12

Name: Problem 44, Chapter 2: Beginning Algebra
Uploaded: 2020-07-20T23:46:24-08:00
Duration: 4 min 22 s
Channel: Shonte Cobbs
Description: Solve inequality. Write the solution set in interval notation, and graph it. 6 t+3<3 t+12

step 1 All right, so we have multiple steps to do in this inequality. So we're going to start out by pu

Solve inequality. Write the solution set in interval...

Key Concepts

Linear Inequalities

Linear inequalities are mathematical expressions involving a linear function where the two sides are related by inequality signs (such as <, >, ?, or ?). They describe a range of values that satisfy the given condition and are fundamental in algebra for modeling situations with limits or bounds.

Algebraic Manipulation in Inequalities

This concept involves using algebraic operations to isolate the variable in an inequality while keeping track of the rules unique to inequalities, such as reversing the inequality sign when multiplying or dividing by a negative number. It is essential for finding the set of all solutions that satisfy the original inequality.

Interval Notation

Interval notation is a concise way to represent subsets of the real numbers, particularly solution sets of inequalities. It uses symbols like parentheses and brackets to denote whether endpoints are excluded or included, respectively, making it a standardized tool for communicating ranges of values.

Graphing on a Number Line

Graphing on a number line involves visually representing the set of solutions of an inequality by marking the relevant portion of the line. Open or closed circles indicate whether endpoints are excluded or included, and shading is used to show the direction in which the inequality holds, helping to provide an intuitive understanding of the solution set.

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