Exploring Linear Inequalities and Absolute Value Graphs

The video tutorial covers absolute value inequalities, starting with an introduction and overview of the topic. It includes a step-by-step solution to an inequality problem, graphing solutions, and using interval notation. The tutorial also explores working backwards from graphs to determine inequalities and applies these concepts to word problems. The session concludes with a reflection on learning and questions for further exploration.

What should you do first when solving an absolute value inequality?

• Multiply both sides by a negative number

• Get the absolute value expression by itself

• Add a constant to both sides

• Square both sides

If an absolute value inequality is 'less than or equal to', what type of problem is it?

• An 'or' problem

• A 'both' problem

• A 'neither' problem

• An 'and' problem

What is the first step in solving the inequality |2x + 8|/5 + 1/4 > 2?

• Subtract 1/4 from both sides

• Multiply by 20 to clear the fraction

• Divide by 5

• Add 2 to both sides

When you multiply or divide by a negative number in an inequality, what must you remember to do?

• Subtract the same number from both sides

• Add the same number to both sides

• Flip the inequality sign

• Square both sides

In interval notation, how would you represent the solution set for x > 0.375 or x < -8.375?

• (-8.375, 0.375)

• (-∞, 0.375) ∪ (0.375, ∞)

• (-∞, 0.375) ∪ (-8.375, ∞)

• (-∞, -8.375) ∪ (0.375, ∞)

What is the 'home base' in an absolute value inequality graph?

• The average of the endpoints

• The midpoint of the endpoints

• The lowest point on the graph

• The highest point on the graph

How do you determine the distance from the home base in an absolute value inequality graph?

• By adding the coordinates of the endpoints

• By measuring the distance from the origin

• By finding the difference between the highest and lowest points

• By calculating the total distance between the endpoints and dividing by 2

If Matt's average golf score is 66 and he scores within 6 strokes of his average, what is the range of his possible scores?

• 60 to 66

• 66 to 72

• 60 to 72

• 62 to 70

What are the possible types of solutions for an absolute value inequality?

• One solution, two solutions, or no solution

• One solution, two solutions, infinite solutions, or no solution

• One solution, infinite solutions, or no solution

• Two solutions, infinite solutions, or no solution

Can an absolute value inequality have only one solution? If so, what might it look like?

• No, it always has infinite solutions

• Yes, when the inequality is strict

• No, it always has two solutions

• Yes, when the absolute value equals zero