Exploring Absolute Value Inequalities Through Word Problems

What is Mark's weight as mentioned in the problem?

• 175 pounds

• 180 pounds

• 170 pounds

• 185 pounds

How many pounds can Mark be off his weight to compete in his weight class?

• 4 pounds

• 3 pounds

• 2 pounds

• 5 pounds

What is the lowest weight Mark can be to compete?

• 171 pounds

• 172 pounds

• 173 pounds

• 170 pounds

What is the highest weight Mark can be to compete?

• 180 pounds

• 176 pounds

• 178 pounds

• 177 pounds

What is the absolute value inequality that represents Mark's weight range?

• |x - 175| ≥ 3

• |x + 175| ≤ 3

• |x + 175| ≥ 3

• |x - 175| ≤ 3

What does the inequality |x - 175| ≤ 3 represent in this context?

• Mark's weight must be more than 3 pounds above 175 pounds.

• Mark's weight must be less than 3 pounds below 175 pounds.

• Mark's weight can be within 3 pounds above or below 175 pounds.

• Mark's weight must be exactly 175 pounds.

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

• Add 3 to both sides

• Multiply both sides by 3

• Subtract 3 from both sides

• Split the inequality into two separate inequalities

What is the solution to the inequality |x - 175| ≤ 3?

• x ≤ 178 and x ≥ 172

• x ≥ 178 and x ≤ 172

• x ≥ 175 and x ≤ 170

• x ≤ 175 and x ≥ 170

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

• A single point at 175

• A shaded region between 172 and 178, including the endpoints

• A shaded region between 170 and 180, including the endpoints

• A shaded region between 170 and 180, excluding the endpoints

Why are the endpoints 172 and 178 shaded on the number line?

• Because the inequality is strict

• Because the inequality includes the endpoints

• Because the inequality excludes the endpoints

• Because the endpoints are not part of the solution