Exploring Absolute Value Equations and Inequalities

The video tutorial covers absolute value equations and inequalities, explaining that absolute value represents the distance from zero, which is always positive. It demonstrates solving absolute value equations by isolating the absolute value expression and considering both positive and negative solutions. The tutorial also covers graphing these solutions on a number line with closed circles. It addresses cases where no solution exists if the absolute value equals a negative number. The video further explores absolute value inequalities, showing how to solve and graph them, including the use of open and closed circles and shading on the number line.

What is the absolute value of -5?

• 0

• -5

• 10

• 5

If the absolute value of x is 7, what are the possible values of x?

• 7 and -14

• 7 and 0

• 7 and -7

• 7 and 14

What is the first step in solving the equation 3|x + 2| = 15?

• Multiply both sides by 3

• Divide both sides by 3

• Subtract 2 from both sides

• Add 2 to both sides

How do you graph the solutions of |x| = 4 on a number line?

• Open circles at -4 and 4

• Closed circles at -4 and 4

• Open circle at 4 only

• Closed circle at 4 only

What does it mean if an absolute value equation equals a negative number?

• There is one solution

• There is no solution

• There are two solutions

• The solution is zero

When solving |x - 3| < 5, what are the two inequalities you need to solve?

• x - 3 < 5 and x - 3 < -5

• x - 3 < 5 and x - 3 > -5

• x - 3 > 5 and x - 3 > -5

• x - 3 > 5 and x - 3 < -5

How do you graph the solution of |x + 1| > 2 on a number line?

• Open circles at -1 and 2 with shading between them

• Closed circles at -1 and 2 with shading between them

• Closed circles at -3 and 1 with shading outside them

• Open circles at -3 and 1 with shading outside them

What type of circle is used to graph x ≤ 4 on a number line?

• Open circle

• Closed circle

• No circle

• Half-filled circle

In the inequality |2x + 3| ≥ 7, what is the first step to solve it?

• Multiply both sides by 2

• Divide both sides by 2

• Add 3 to both sides

• Subtract 3 from both sides

What is the solution set for the inequality |x - 4| ≤ 6?

• x ≤ -10 or x ≥ 2

• -10 ≤ x ≤ 2

• x ≤ -2 or x ≥ 10

• -2 ≤ x ≤ 10