Inequalities and Number Line Representation

The video tutorial explains how to solve one-step inequalities by isolating the variable. It demonstrates graphing solutions on a number line, using open circles for inequalities without equality and closed circles for those with equality. The tutorial covers solving for X and Y, emphasizing the importance of shading the correct region to represent the solution set.

What is the first step in solving the inequality X - 5 > -7?

• Add 5 to both sides

• Multiply both sides by 5

• Subtract 5 from both sides

• Divide both sides by 5

After isolating X, what inequality do we get?

• X > -7

• X < -7

• X = -7

• X ≤ -7

How do we represent X > -7 on a number line?

• Closed circle at -7, shade to the left

• Open circle at -7, shade to the left

• Open circle at -7, shade to the right

• Closed circle at -7, shade to the right

Why do we shade to the right for X > -7?

• It represents all points less than -7

• It represents all points not equal to -7

• It represents all points greater than -7

• It represents all points equal to -7

Which point can be used to verify the solution X > -7?

• -10

• -7

• -8

• 0

What operation is performed to solve for Y in the inequality Y + 4 ≤ 5?

• Multiply both sides by 4

• Subtract 4 from both sides

• Add 4 to both sides

• Divide both sides by 4

What is the resulting inequality after solving for Y?

• Y = 5

• Y ≤ 5

• Y > 5

• Y < 5

How is Y ≤ 5 represented on a number line?

• Closed circle at 5, shade to the left

• Open circle at 5, shade to the right

• Open circle at 5, shade to the left

• Closed circle at 5, shade to the right

Why do we use a closed circle for Y ≤ 5?

• Because 5 is not part of the solution

• Because 5 is part of the solution

• Because Y is greater than 5

• Because Y is less than 5

In the inequality Y ≤ 5, which direction do we shade on the number line?

• No shading

• Both directions

• To the left

• To the right