Solving Absolute Value Inequalities

The video tutorial explains how to solve absolute value inequalities, specifically when the inequality involves a greater than symbol. It covers the process of splitting the inequality into two separate inequalities, solving each one, and graphing the solution set on a number line. The tutorial emphasizes the importance of the 'or' condition in such inequalities and provides a step-by-step guide to solving and graphing the solutions.

What is the initial inequality problem discussed in the video?

• The absolute value of 2x - 7 is less than 3

• The absolute value of 2x - 7 is greater than 3

• The absolute value of 2x + 7 is greater than 3

• The absolute value of 2x + 7 is less than 3

What happens when you have an absolute value inequality with a 'greater than' symbol?

• You use the word 'and' between two inequalities

• You use the word 'or' between two inequalities

• You solve it as a single inequality

• You ignore the absolute value

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

• Rewrite the inequality without the absolute value

• Rewrite the inequality with the absolute value

• Multiply both sides by a negative number

• Add a constant to both sides

How do you solve the inequality 2x - 7 > 3?

• Divide both sides by 2

• Multiply both sides by 2

• Add 7 to both sides

• Subtract 7 from both sides

What is the solution for x in the inequality 2x - 7 > 3?

• x < 2

• x > 2

• x < 5

• x > 5

What is the second inequality derived from the absolute value inequality?

• 2x - 7 < -3

• 2x - 7 > -3

• 2x + 7 < 3

• 2x + 7 > 3

How do you solve the inequality 2x - 7 < -3?

• Add 7 to both sides

• Multiply both sides by 2

• Divide both sides by 2

• Subtract 7 from both sides

What is the solution for x in the inequality 2x - 7 < -3?

• x > 5

• x < 5

• x > 2

• x < 2

What word is used to combine the solutions of the two inequalities?

• And

• But

• Or

• Nor

How is the solution represented on a number line for x < 2?

• Circle at 2, shade to the left

• Filled circle at 2, shade to the left

• Circle at 2, shade to the right

• Filled circle at 2, shade to the right