Solving Absolute Value Equations and Inequalities

This video tutorial covers solving absolute value equations and inequalities. It begins with an introduction to the concept of absolute value, followed by detailed steps to solve equations and graph solutions. The tutorial also explains sandwich problems and provides advanced examples to reinforce learning.

What is the basic rule for absolute value?

• It is always less than zero.

• It is always equal to zero.

• It is always greater than or equal to zero.

• It can be any real number.

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

• Add a constant to both sides.

• Write down the equation without the absolute value sign.

• Multiply both sides by a constant.

• Divide both sides by a constant.

When solving absolute value inequalities, what must you do after writing down the equation without the absolute value sign?

• Divide both sides by a constant.

• Multiply both sides by a constant.

• Flip the sign and make it negative.

• Add a constant to both sides.

How do you represent a solution that is greater than a certain value on a graph?

• With an open hole and shading to the left.

• With a closed hole and shading to the right.

• With an open hole and shading to the right.

• With a closed hole and shading to the left.

What does it mean when two shaded regions meet in the center on a graph?

• The solution is an empty set.

• The solution is invalid.

• It represents a 'sandwich' inequality.

• The solution is a single point.

How do you combine two inequalities into a single 'sandwich' inequality?

• Subtract one inequality from the other.

• Add the inequalities together.

• Combine them from least to greatest.

• Write the inequalities separately.

What is the solution to the inequality |X + 4| ≤ 6?

• -6 ≤ X ≤ 4

• X ≤ -10 or X ≥ 2

• X ≤ -6 or X ≥ 4

• -10 ≤ X ≤ 2

How do you graph the solution to the inequality |2X - 3| < 5?

• Shade between -1 and 4 with open holes.

• Shade between -1 and 4 with closed holes.

• Shade to the left of -1 and to the right of 4 with open holes.

• Shade to the left of -1 and to the right of 4 with closed holes.

What is the solution to the inequality |2X - 5| > 1?

• X < 2 or X > 3

• X < 2 or X > 4

• X < -2 or X > 3

• X < 1 or X > 2

What is the solution to the inequality |3X + 2| ≤ 7?

• -3 ≤ X ≤ 5/3

• -7/3 ≤ X ≤ 3

• -5/3 ≤ X ≤ 3

• -3 ≤ X ≤ 7/3