Graph the solution set, and write it using interval notation. -3(x-6)>2 x-2

Name: Problem 37, Chapter 8: Beginning and Intermediate Algebra
Uploaded: 2022-02-13T17:39:00-08:00
Duration: 38 s
Channel: James Kiss
Description: Graph the solution set, and write it using interval notation. -3(x-6)>2 x-2

step 1 Given negative 3 times the quantity x minus 6 greater than 2x minus 2, distribute the negative 3

Graph the solution set, and write it using interval...

Key Concepts

Linear Inequalities

This concept involves inequalities that contain linear expressions. Solving a linear inequality is similar to solving a linear equation but requires careful handling of the inequality sign during operations, especially when multiplying or dividing by a negative number.

Algebraic Manipulation

This refers to applying operations such as distribution, adding, subtracting, and combining like terms to both sides of an inequality. The goal is to isolate the variable on one side, ensuring the inequality remains true for all values in its solution set.

Multiplying or Dividing by a Negative Number

A key concept in solving inequalities, this rule states that when both sides of an inequality are multiplied or divided by a negative number, the direction of the inequality symbol must be reversed. This ensures that the relationship between the expressions remains valid.

Graphical Representation on a Number Line

This involves visually depicting the solution set of an inequality on a number line. It helps in understanding the range of values that satisfy the inequality, with open circles or parentheses indicating that an endpoint is not included and closed circles or brackets indicating that it is.

Interval Notation

This is a concise way to represent the set of solutions for an inequality using intervals. Parentheses are used to denote endpoints that are not included in the solution set, while square brackets indicate included endpoints. It provides a clear and standardized method to express the range of values involved.

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