Understanding Inequalities and Interval Notation

This video tutorial covers solving one-step linear inequalities in one variable. It explains how to express solutions as inequalities, graphs, and using interval notation. The tutorial provides examples of different inequalities and demonstrates how to solve them, including the special rule of reversing the inequality symbol when multiplying or dividing by a negative number.

What is the primary goal of the lesson on solving one-step linear inequalities?

• To graph quadratic functions

• To learn about polynomial division

• To solve one-step linear inequalities

• To solve quadratic equations

Which of the following is NOT a way to express the solution of an inequality?

• Using interval notation

• As a polynomial

• As a graph

• As an inequality

How is an open point represented in interval notation?

• With a square bracket

• With a rounded parenthesis

• With a curly brace

• With a straight line

What does a closed point on a graph indicate about the interval?

• The interval is undefined

• The value is included

• The interval is infinite

• The value is not included

What is the interval notation for x greater than zero?

• (0, ∞)

• (-∞, 0)

• [0, ∞]

• [0, ∞)

In the inequality x ≤ 3, how is the number 3 represented on the graph?

• As a dashed line

• As a shaded region

• As an open point

• As a closed point

What is the interval notation for x less than or equal to 3?

• (-∞, 3)

• [3, ∞)

• (3, ∞)

• (-∞, 3]

When solving inequalities, what must you do if you multiply or divide by a negative number?

• Add a constant to both sides

• Reverse the inequality symbol

• Square both sides

• Subtract a constant from both sides

Why do we reverse the inequality symbol when dividing by a negative number?

• Because it is a rule for all mathematical operations

• Because negative numbers are always less than positive numbers

• Because it helps in graphing the inequality

• Because it makes the equation easier to solve

Which of the following is true about the inequality -2 < 4?

• It is false because both numbers are negative

• It is true because both numbers are positive

• It is true because negative numbers are less than positive numbers

• It is false because -2 is greater than 4