Exploring Absolute Value Equations and Inequalities

The video tutorial covers the concept of absolute value, explaining it as the distance of a number from zero on a number line. It provides examples of solving absolute value equations and inequalities, including cases with different origins and negative centers. The tutorial also discusses real-world applications, such as determining temperature ranges for a reptile's enclosure, and emphasizes the importance of understanding the mathematical language and processes involved.

What is the absolute value of -5?

• 0

• 5

• -5

• 10

If the absolute value of a number is 7, which of the following could be the number?

• Both -7 and 7

• -7

• 0

• 7

In the equation |x - 7| = 3, what are the possible values of x?

• 3 and 7

• 4 and 10

• 4 and 7

• 7 and 10

How do you solve the equation |x + 3| = 5?

• x = 2 or x = -8

• x = 5 or x = -5

• x = 2 or x = -2

• x = 8 or x = -2

Why does the equation |x + 3| = -5 have no solution?

• Because x cannot be negative

• Because absolute value cannot be negative

• Because absolute value is always zero

• Because x cannot be positive

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

• Distribute into the absolute value

• Add a constant to both sides

• Isolate the absolute value

• Multiply both sides by a constant

If the ideal temperature for a reptile is 80°F with a tolerance of ±10°F, what is the maximum temperature?

• 100°F

• 80°F

• 90°F

• 70°F

How do you represent the temperature range for the reptile's comfort mathematically?

• |x + 80| ≤ 10

• |x + 10| ≤ 80

• |x - 80| ≤ 10

• |x - 10| ≤ 80

What does the inequality |x - 80| > 10 represent in the context of the reptile's temperature?

• Temperatures that are less than 10°F away from 80°F

• Temperatures that are more than 10°F away from 80°F

• Temperatures that are within 10°F of 80°F

• Temperatures that are exactly 80°F

If the temperature is less than 70°F or greater than 90°F, what does it mean for the reptile?

• The reptile is in a safe range

• The reptile is in ideal conditions

• The reptile is at risk

• The reptile is comfortable