Solving Absolute Value Inequalities

What is the main difference between absolute value equations and absolute value inequalities?

• Inequalities provide a single solution.

• Equations provide a range of solutions.

• Inequalities provide a range of solutions.

• Equations are always graphed.

What is the first step in solving absolute value inequalities?

• Determine if it's 'and' or 'or'.

• Isolate the absolute value.

• Graph the solution.

• Flip the inequality.

When solving absolute value inequalities, what does 'less than' indicate?

• An 'or' statement.

• A 'not equal to' statement.

• A 'between' statement.

• A 'greater than' statement.

How do you write a 'between' statement for an 'and' inequality?

• Write the absolute value expression once with 'equal to' signs.

• Write the absolute value expression twice with 'not equal to' signs.

• Write the absolute value expression in the middle of two 'less than' signs.

• Write the absolute value expression twice with 'greater than' signs.

In the example of solving 'and' inequalities, what is the final solution for |3x + 4| ≤ 8?

• -4 ≤ x ≤ 4/3

• -4 ≤ x ≤ 4

• -12 ≤ x ≤ 4

• -4 ≤ x ≤ 8

What does 'greater than' indicate when solving absolute value inequalities?

• An 'or' statement.

• A 'between' statement.

• An 'and' statement.

• A 'not equal to' statement.

In the example of solving 'or' inequalities, what is the final solution for |2x - 6| > 14?

• x > -4 or x < 7

• x > -4 or x < 10

• x < -4 or x > 10

• x < -4 or x > 7

Why is it important to isolate the absolute value before determining 'and' or 'or'?

• To avoid errors in arithmetic.

• To make graphing easier.

• To ensure the correct inequality type is identified.

• To simplify the equation.

In the complex example, what is the final solution for -1/2|4x - 2| ≥ -7?

• -3 ≤ x ≤ 4

• -4 ≤ x ≤ 3

• -3 ≤ x ≤ 4

• -4 ≤ x ≤ 3

What is the assignment given at the end of the tutorial?

• Pages 36-37, problems 16-27 and 44-53

• Pages 36-37, problems 1-15 and 28-40

• Pages 38-39, problems 1-15 and 28-40

• Pages 38-39, problems 16-27 and 44-53