Solving Absolute Value Inequalities

What is the primary goal of this lesson?

• To learn about polynomial functions

• To understand linear equations

• To solve quadratic equations

• To write and solve absolute value inequalities

In an absolute value inequality, what must you do when you make the other value negative in case two?

• Subtract 1 from the value

• Add 1 to the value

• Flip the sign

• Keep the sign the same

When graphing the inequality |x| < 3, what type of compound inequality is it?

• Or

• And

• Neither

• Both

What is the solution to the inequality |2n + 3| ≤ 5?

• n ≤ 1 and n ≥ -4

• n ≥ 1 and n ≤ -4

• n ≤ 1 or n ≥ -4

• n ≥ 1 or n ≤ -4

What is a common error when solving absolute value inequalities?

• Using the wrong variable

• Forgetting to isolate the absolute value

• Adding instead of subtracting

• Multiplying instead of dividing

If the absolute value of a number is less than or equal to a negative number, what is the solution?

• No solution

• Depends on the number

• Sometimes true

• Always true

What is the inequality for the debate team's hotel cost problem?

• |4x - 175| ≤ 20

• |4x + 175| ≤ 20

• |4x - 200| ≤ 20

• |4x + 200| ≤ 20

Which hotel can the debate team consider if their budget is within $20 of $175?

• Hotel A and Hotel C

• Hotel B and Hotel C

• Hotel A and Hotel B

• Hotel A only

If the debate team's budget increases to $200 ± $20, can they afford Hotel D at $55 per night?

• Yes, because the total cost is within the range

• No, because the total cost is less than $200

• No, because the total cost exceeds the range

• Yes, because the total cost is exactly $200

What is the correct way to write the solution for an 'and' compound inequality?

• x > a or x < b

• x > a and x < b

• x < a or x > b

• x < a and x > b