Solving and Graphing Absolute Value Inequalities

The video tutorial explains how to solve an absolute value inequality by isolating the absolute value, setting up compound inequalities, and solving them. It demonstrates how to express the solution as a compound inequality, graph, and using interval notation. The process involves undoing operations to isolate the absolute value, setting up two inequalities connected by 'or', solving them, and graphing the solution. The tutorial concludes with expressing the solution using interval notation.

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

• Multiply both sides by a constant

• Add a constant to both sides

• Reverse the inequality symbol

• Isolate the absolute value on one side of the inequality

In the inequality 2|x + 2| - 3 > 5, what should be done first to isolate the absolute value?

• Add 3 to both sides

• Multiply both sides by 2

• Divide both sides by 2

• Subtract 3 from both sides

After isolating the absolute value, what is the next step in solving 2|x + 2| > 8?

• Divide both sides by 2

• Subtract 2 from both sides

• Multiply both sides by 2

• Add 2 to both sides

What does the absolute value inequality |x + 2| > 4 mean in terms of distance from zero?

• x + 2 is less than 4 units from 0

• x + 2 is more than 4 units from 0

• x + 2 is less than or equal to 4 units from 0

• x + 2 is exactly 4 units from 0

How do you set up the compound inequalities from |x + 2| > 4?

• x + 2 > 4 and x + 2 < -4

• x + 2 < 4 or x + 2 > -4

• x + 2 > 4 or x + 2 < -4

• x + 2 < 4 and x + 2 > -4

What is the solution to the inequality x + 2 > 4?

• x < -2

• x < 2

• x > 2

• x > -2

What is the solution to the inequality x + 2 < -4?

• x < 6

• x > -6

• x < -6

• x > 6

How is the solution to the compound inequality represented on a graph?

• Open points on 2 and -6 with arrows pointing outward

• Closed points on 2 and -6 with arrows pointing inward

• Open points on 2 and -6 with arrows pointing inward

• Closed points on 2 and -6 with arrows pointing outward

What does the union of the intervals x > 2 and x < -6 represent?

• The difference of the intervals

• The complement of the intervals

• The combined solution of the intervals

• The intersection of the intervals

How is the interval notation for the solution x > 2 or x < -6 written?

• (-∞, -6) ∩ (2, ∞)

• (-∞, -6) ∪ (2, ∞)

• (-∞, -6] ∪ (2, ∞)

• (-∞, -6) ∪ [2, ∞)