Solving Inequalities and Absolute Values

This video tutorial introduces absolute value inequalities, focusing on less than inequalities. It explains how to interpret these inequalities using number lines and convert them into compound inequalities. The video provides a step-by-step guide to solving absolute value inequalities, including a detailed example problem. The tutorial emphasizes understanding the concept of distance on a number line and converting inequalities into a form that is easier to solve.

What type of inequalities are focused on in this video?

• Greater than inequalities

• Less than inequalities

• Equal to inequalities

• Not equal to inequalities

What does the absolute value inequality |x| < 3 represent on a number line?

• Values equal to 3 units from 0

• Values more than 3 units from 0

• Values less than 3 units from 0

• Values exactly 3 units from 0

How is the inequality |x| < 3 converted into a compound inequality?

• x ≤ 3 and x ≥ -3

• x < 3 and x > -3

• x = 3 or x = -3

• x > 3 and x < -3

What is the general rule for solving absolute value inequalities of the form |U| < a?

• U = a or U = -a

• U < a and U > -a

• U < a or U > -a

• U > a and U < -a

In the inequality |U| < 2, what values are not included in the solution set?

• All values are included

• 2 and -2

• 1 and -1

• 0 and 2

What is the solution set for the inequality |U| < 2 when converted to a compound inequality?

• U > 2 and U < -2

• U < 2 and U > -2

• U = 2 or U = -2

• U ≤ 2 and U ≥ -2

What is the first step in solving the inequality 1 + 4T < 2 and 1 + 4T > -2?

• Divide by 4

• Multiply by 4

• Add 1 to both sides

• Subtract 1 from both sides

After subtracting 1 from both sides in the inequality 1 + 4T < 2, what is the next step?

• Divide by 4

• Add 1 to both sides

• Multiply by 4

• Subtract 4 from both sides

What is the final solution for T in the inequality 1 + 4T < 2 and 1 + 4T > -2?

• T = 1/4 or T = -3/4

• T > 1/4 and T < -3/4

• T < 1/4 and T > -3/4

• T ≤ 1/4 and T ≥ -3/4

How can the solution set for the inequality |U| < 2 be expressed in interval notation?

• (-2, 2)

• [2, -2]

• (-∞, 2)

• [2, ∞)