Solving Absolute Value Inequalities: And vs Or

This video tutorial covers how to solve absolute value inequalities, explaining the concept of absolute value as a measure of distance from zero. It distinguishes between inequalities where the absolute value is greater than or less than a given number, using examples to illustrate each case. The tutorial provides step-by-step instructions for solving these inequalities and demonstrates how to graph the solutions on a number line. It also addresses more complex problems and offers additional resources for further learning.

What does the absolute value of a number represent?

• The distance from zero

• The number itself

• The square of the number

• The negative of the number

If the absolute value of x is greater than 4, what does it mean?

• x is between -4 and 4

• x is exactly 4

• x is less than -4 or greater than 4

• x is exactly -4

In mathematical terms, what does 'or' signify?

• Intersection

• Union

• Difference

• Complement

How do you split the inequality |2x - 3| ≥ 1?

• 2x - 3 ≥ 1 and 2x - 3 ≤ -1

• 2x - 3 ≤ 1 or 2x - 3 ≥ -1

• 2x - 3 ≥ 1 or 2x - 3 ≤ -1

• 2x - 3 ≤ 1 and 2x - 3 ≥ -1

What is the solution set for |2x - 3| ≥ 1?

• x ≤ 2 or x ≥ 1

• x ≥ 2 and x ≤ 1

• x ≤ 2 and x ≥ 1

• x ≥ 2 or x ≤ 1

How do you graphically represent the solution of |5x + 1| ≤ 6?

• x ≤ 1 or x ≥ -7/5

• x ≥ 1 and x ≤ -7/5

• x ≤ 1 and x ≥ -7/5

• x ≥ 1 or x ≤ -7/5

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

• Graph the solution

• Flip the inequality sign

• Combine the inequalities

• Isolate the absolute value expression

For the inequality |3x - 2| > 7, what are the two inequalities you need to solve?

• 3x - 2 < 7 and 3x - 2 > -7

• 3x - 2 > 7 and 3x - 2 < -7

• 3x - 2 < 7 or 3x - 2 > -7

• 3x - 2 > 7 or 3x - 2 < -7

What does 'and' signify in mathematical terms?

• Complement

• Difference

• Union

• Intersection

How do you write the solution set for |4x + 3| ≤ 9?

• x ≥ -3 and x ≤ 3/2

• -3 ≥ x ≥ 3/2

• x ≤ -3 or x ≥ 3/2

• -3 ≤ x ≤ 3/2