Understanding Absolute Value Inequalities

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

• Add the word 'or' between inequalities

• Isolate the absolute value expression

• Multiply both sides by a constant

• Graph the inequality on a number line

When creating two inequalities from an absolute value expression, what must you do to the second inequality?

• Keep the inequality sign the same

• Add a constant to both sides

• Flip the inequality sign and make the right side negative

• Multiply both sides by -1

How do you represent a solution where the shading is in the middle on a number line?

• Use the word 'or' between inequalities

• Use a closed dot on the number line

• Use the word 'and' between inequalities

• Shade only one side of the number line

In Example 2, what operation is performed first to isolate the absolute value?

• Divide by 8

• Subtract 2

• Add 2

• Multiply by 8

What is the result of dividing both sides of an inequality by a negative number?

• The inequality sign flips

• The inequality becomes an equation

• The inequality sign becomes a less than sign

• The inequality sign remains the same

In Example 3, what is the first step after isolating the absolute value?

• Multiply both sides by 2

• Create two separate inequalities

• Add 17 to both sides

• Graph the solution

What does an open dot on a number line indicate?

• The inequality is a strict inequality

• The inequality is an equation

• The number is not included in the solution

• The number is included in the solution

How do you determine if the word 'or' should be used between inequalities?

• If the inequality is non-strict

• If the inequality is strict

• If the shading is on the outside

• If the shading is in the middle

What is the purpose of graphing inequalities on a number line?

• To simplify the inequality

• To check for errors in calculation

• To visually represent the solution set

• To find the exact solution

In Example 3, what is the final step after solving the inequalities?

• Multiply the solutions by a constant

• Add the solutions together

• Graph the solution on a number line

• Check the solution with the original inequality