Solving Inequalities: Adding and Subtracting Techniques

The video tutorial covers solving inequalities by adding or subtracting, building on previous lessons about solving one-step and two-step equations. It introduces graphing solutions as an additional step. The tutorial provides examples, such as solving y plus 7 is greater than or equal to 12 and y minus 3 is less than 4, demonstrating how to graph these inequalities on a number line. The video emphasizes understanding the direction of inequalities and the use of open or closed circles to represent solutions.

What is the first step in solving inequalities similar to?

• Graphing the solution

• Finding the least common denominator

• Solving one-step equations

• Multiplying both sides

What is the significance of graphing inequalities?

• It helps in visualizing the solution set

• It is only for aesthetic purposes

• It changes the solution

• It is not necessary

What operation is performed to both sides when subtracting 10 from an inequality?

• Division

• Addition

• Subtraction

• Multiplication

What does the direction of the arrow on a graph indicate?

• The exact value of the solution

• The range of possible solutions

• The maximum value of the solution

• The minimum value of the solution

How is 'greater than or equal to' represented on a graph?

• With an open circle

• With an arrow pointing left

• With a dashed line

• With a solid circle

Why do we add 7 when solving y + 7 > 12?

• To isolate the variable on one side

• To comply with the rules of algebra

• To make the inequality false

• To eliminate the variable

What does an open circle on a graph indicate?

• Less than

• Greater than or equal to

• Greater than

• Equal to

What does a filled circle on a graph symbolize?

• The inequality is only true for one value

• The variable is exactly equal to the number

• The variable is not included in the solution

• The solution includes the number

In the context of inequalities, what does subtracting 4 from both sides accomplish?

• It increases the value of the variable

• It decreases the value of the variable

• It cancels out the addition of 4

• It changes the direction of the inequality

When graphing y - 3 < 4, why do we add 3 to both sides?

• To isolate y and solve the inequality

• To determine the slope of the graph

• To find the maximum value of y

• To simplify the inequality