Solving Absolute Value Inequalities with DeltaMath

The video tutorial covers solving absolute value inequalities. It begins by explaining how to handle inequalities by treating them as equalities and solving for positive and negative cases. The tutorial uses a number line to illustrate solutions and discusses the concept of open and closed dots for graphing inequalities. A second example is provided, demonstrating the process of solving and graphing absolute value inequalities with less than or equal to conditions. The video emphasizes checking solutions in different regions and understanding the direction of inequalities.

What is the first step in solving an absolute value inequality?

• Ignore the inequality sign

• Multiply both sides by -1

• Graph the inequality

• Add 3 to both sides

When solving the equation X - 3 = 9, what are the two possible values of X?

• X = 9 and X = -9

• X = 12 and X = 6

• X = 12 and X = -6

• X = 6 and X = -6

What type of dot is used on the number line for a 'greater than' inequality?

• Open dot

• Closed dot

• Solid dot

• Shaded dot

If X - 3 > 9, which region on the number line will be false?

• Between -6 and 12

• To the right of 12

• To the left of -6

• None of the above

For the inequality X - 3 > 9, which number would make the inequality true when tested on the right side of 12?

• 10

• 0

• 15

• 5

In the second example, what are the boundaries for the graph when solving X - 1 = 10?

• X = 9 and X = -11

• X = 10 and X = -10

• X = 11 and X = -9

• X = 12 and X = -8

What type of dot is used for 'less than or equal to' inequalities on the number line?

• Solid dot

• Open dot

• Closed dot

• Shaded dot

Which number would make the inequality X - 1 ≤ 10 true when tested in the center region?

• 20

• 12

• 0

• 15

For the inequality X - 1 ≤ 10, which number would make the inequality false when tested on the right side of 11?

• 15

• 0

• 10

• 5

How is the final solution written for the inequality X - 1 ≤ 10?

• X < -9 or X > 11

• X ≤ -9 or X ≥ 11

• X ≥ -9 and X ≤ 11

• X > -9 and X < 11