Solving Absolute Value Inequalities

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

• Add a constant to both sides

• Isolate the absolute value bars

• Flip the inequality sign

• Multiply both sides by a constant

When solving the inequality |3p - 12| < 9, what are the two cases you need to consider?

• 3p - 12 < 9 and 3p - 12 < -9

• 3p - 12 < 9 and 3p - 12 > -9

• 3p - 12 < 9 and 3p - 12 > 9

• 3p - 12 < 9 and 3p - 12 > 0

What type of inequality is represented by the symbol '<' in absolute value inequalities?

• And inequality

• Inclusive inequality

• Or inequality

• Exclusive inequality

How do you write the solution to |x| < 9 in set-builder notation?

• {x | x > -9 and x < 9}

• {x | x < -9 or x > 9}

• {x | x > -9 or x < 9}

• {x | -9 < x < 9}

What does an 'and' inequality graph look like?

• A single point on the number line

• Two overlapping rays

• A single line segment between two points

• Two rays going in opposite directions

When solving the inequality |x - 5| > 4, what are the two cases you need to consider?

• x - 5 < 4 and x - 5 < -4

• x - 5 > 4 and x - 5 > -4

• x - 5 > 4 and x - 5 < -4

• x - 5 < 4 and x - 5 > -4

What type of inequality is represented by the symbol '>' in absolute value inequalities?

• Inclusive inequality

• Or inequality

• Exclusive inequality

• And inequality

How do you write the solution to |x - 5| > 4 in set-builder notation?

• {x | x < 9 and x > 1}

• {x | x > 9 or x < 1}

• {x | x < 9 or x > 1}

• {x | x > 9 and x < 1}

In a word problem involving absolute value inequalities, what does the term 'within' typically indicate?

• A single value

• An 'or' inequality

• An 'and' inequality

• An exclusive range

How would you write the compound inequality for the range 3.75 to 4.25?

• 3.75 < x < 4.25

• 3.75 > x > 4.25

• 3.75 ≤ x ≤ 4.25

• 3.75 ≥ x ≥ 4.25