Understanding Absolute Value Inequalities

The video tutorial explains how to solve an inequality involving the absolute value of p. It begins by isolating the absolute value expression and then explains the concept of absolute value using a number line. The tutorial proceeds to solve the compound inequality and verifies the solution with examples, ensuring the solution set is correct.

What is the first step in solving the inequality |p - 12| + 4 < 14?

• Divide both sides by 4

• Multiply both sides by 4

• Subtract 4 from both sides

• Add 4 to both sides

What does the inequality |x| < 10 imply about the distance of x from 0?

• x is more than 10 units away from 0

• x is exactly 10 units away from 0

• x is exactly 0 units away from 10

• x is less than 10 units away from 0

How can the inequality |x| < 10 be rewritten?

• x = 10

• x < -10 or x > 10

• x = -10

• -10 < x < 10

What is the next step after rewriting |p - 12| < 10 as a compound inequality?

• Divide all parts by 12

• Multiply all parts by 12

• Subtract 12 from all parts of the inequality

• Add 12 to all parts of the inequality

What is the solution to the inequality -10 < p - 12 < 10?

• p > 2 and p < 22

• p < 2 and p > 22

• p = 2 or p = 22

• p = 0

How is the solution to the inequality represented on a number line?

• A filled circle at 2 and 22

• A line from 2 to 22 with open circles

• An open circle at 2 and 22

• A line from 2 to 22 with filled circles

Which value of p is within the solution set of the inequality?

• p = 2

• p = 22

• p = 0

• p = 12

What happens when p = 0 is tested in the original inequality?

• The inequality becomes an equation

• The inequality does not hold true

• The inequality is undefined

• The inequality holds true

What is the result of testing p = 12 in the inequality |p - 12| + 4 < 14?

• The inequality is undefined

• The inequality does not hold true

• The inequality becomes an equation

• The inequality holds true

Why does p = 0 not satisfy the inequality |p - 12| + 4 < 14?

• Because 4 is not less than 14

• Because 0 is not less than 14

• Because 16 is not less than 14

• Because 12 is not less than 14