Exploring Absolute Value Inequalities

What does absolute value represent?

• The negative of a number

• The distance from zero on a number line

• The reciprocal of a number

• The square of a number

If the absolute value of x is less than 5, which of the following is true?

• x is equal to 5

• x is greater than 5

• x is less than -5

• x is between -5 and 5

Which conjunction is used when the absolute value of x is less than a given number?

• But

• And

• Or

• Nor

If the absolute value of x is greater than or equal to 7, which of the following is true?

• x is greater than or equal to 7 or less than or equal to -7

• x is less than 7

• x is equal to 0

• x is between -7 and 7

Which conjunction is used when the absolute value of x is greater than or equal to a given number?

• Or

• Nor

• But

• And

For the inequality |x + 3| < 11, what is the range of x?

• x is greater than 11

• x is between -14 and 8

• x is between -11 and 11

• x is less than -11

How do you solve the inequality |3x - 1| ≥ 8?

• 3x - 1 is between -8 and 8

• 3x - 1 is greater than or equal to 8 or less than or equal to -8

• 3x - 1 is less than 8

• 3x - 1 is equal to 0

What is the solution for the inequality |3x - 12| ≤ 2?

• x is greater than 14/3

• x is less than 10/3

• x is equal to 0

• x is between 10/3 and 14/3

Why is it important to understand the reasoning behind solving absolute value inequalities?

• To avoid using conjunctions

• To memorize the steps

• To apply the correct pattern

• To ensure the solution makes sense

What should you check after solving an absolute value inequality?

• Neither the boundary points nor the shading

• Both the boundary points and the shading

• Only the shading

• Only the boundary points