Solving Absolute Value Inequalities in Algebra 1

What does the absolute value of x being less than 2 mean?

• The distance between x and 0 is less than 2.

• The distance between x and 0 is exactly 2.

• The distance between x and 0 is greater than 2.

• The distance between x and 0 is less than or equal to 2.

When solving the absolute value of ax + b is less than c, what type of compound inequality do we use?

• A single inequality

• An and statement

• An or statement

• A quadratic inequality

What happens to the inequality symbol when you multiply or divide an inequality by a negative number?

• It becomes an equal sign

• It becomes a greater than sign

• It stays the same

• It flips

In the inequality |x + 7| ≤ 2, what is the correct way to 'unwrap' the absolute value?

• x + 7 ≤ 2 or x + 7 ≥ -2

• x + 7 ≥ 2 or x + 7 ≤ -2

• x + 7 ≥ 2 and x + 7 ≤ -2

• x + 7 ≤ 2 and x + 7 ≥ -2

What is the solution to the inequality |8x - 11| < 0?

• x < 0

• x > 0

• No solution

• All real numbers

For the inequality |10 - m| ≥ -2, what is the solution?

• m < 10

• m > 10

• No solution

• All real numbers

How do you isolate the absolute value expression in the inequality 4|2x - 5| > 20?

• Subtract 4 from both sides

• Add 4 to both sides

• Multiply both sides by 4

• Divide both sides by 4

What is the graph of the solution to the inequality |2x - 5| > 5?

• x > 5 or x < -5

• x > 5 or x < 0

• x < 5 and x > -5

• x > 5 and x < -5

What is the absolute deviation of a number x from a given value?

• The absolute value of the difference between x and the given value

• The sum of x and the given value

• The absolute value of x

• The difference between x and the given value

If the mean price of computers is $664, what is the price range you are willing to pay with an absolute deviation of at most $100?

• $564 to $764

• $464 to $864

• $664 to $764

• $564 to $664