Understanding Absolute Value Inequalities

The video tutorial explains how to solve absolute value inequalities by setting up two cases: one without the absolute value bars and another by flipping the inequality and changing the sign. It highlights the importance of flipping the inequality when dividing by a negative number. The tutorial also demonstrates how to graph the solution on a number line, emphasizing the difference between 'or' and 'and' solutions.

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

• Graph the inequality

• Multiply by a constant

• Set up two cases

• Combine like terms

When solving the first inequality, what must you remember to do when dividing by a negative number?

• Subtract the same number from both sides

• Multiply by a positive number

• Flip the inequality sign

• Add the same number to both sides

What is the result of dividing -6 by -3 in the first inequality?

• -6

• 6

• -2

• 2

What happens to the inequality sign when dividing by a negative number?

• It flips direction

• It stays the same

• It becomes a greater than sign

• It becomes an equal sign

In the second inequality, what is the value of x after solving?

• x is less than or equal to -6

• x is greater than or equal to 6

• x is less than or equal to 6

• x is greater than or equal to -2

What does a solid dot on the number line indicate?

• The value is not included

• The value is a midpoint

• The value is an estimate

• The value is included

How do you determine the shading direction on the number line?

• Shade towards the larger numbers

• Shade towards the smaller numbers

• Shade away from the points

• Shade between the two points

Why is the solution considered an 'or' problem?

• Because it involves multiplication

• Because it involves subtraction

• Because it involves addition

• Because it involves two separate cases

What is the significance of the coefficient being negative in the inequality?

• It simplifies the inequality

• It requires flipping the inequality

• It makes the inequality unsolvable

• It changes the variable