Exploring Absolute Value Equations and Inequalities

This video tutorial covers solving absolute value equations and inequalities. It begins with isolating the absolute value expression and then solving by creating equivalent linear equations or inequalities. The tutorial includes graphing solutions and applying these concepts to real-world problems. It also explains how to handle compound inequalities and provides a review with practice problems.

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

• Distribute any coefficients

• Add a constant to both sides

• Combine like terms

• Isolate the absolute value expression

When solving the absolute value equation |x| = 7, what are the two possible values of x?

• 7 and -7

• 7 and 0

• 7 and 14

• 7 and -14

In the equation |2x - 5| = 13, what are the two separate equations you need to solve?

• 2x - 5 = 13 and 2x + 5 = 13

• 2x + 5 = 13 and 2x - 5 = 0

• 2x - 5 = 0 and 2x + 5 = -13

• 2x - 5 = 13 and 2x - 5 = -13

What does the 80 represent in the equation D = 80 - 5t?

• The time in seconds

• The starting distance from you

• The final distance from you

• The speed of the skater

Why does the equation |2z + 9| = -2/3 have no solution?

• Because 2z + 9 cannot be negative

• Because the equation is not set up correctly

• Because absolute value cannot be negative

• Because 2z + 9 is always positive

What is the range of allowable weight for a box of crackers that should weigh 213 grams, with a tolerance of 5 grams?

• 200 to 220 grams

• 205 to 225 grams

• 210 to 215 grams

• 208 to 218 grams

How do you set up a compound inequality for |n - 1| < 2?

• -2 > n - 1 > 2

• n - 1 < 2 or n - 1 > -2

• n - 1 < 2 and n - 1 > -2

• -2 < n - 1 < 2

What is the difference between solving |x - 1| < 2 and |x - 1| > 2?

• The first is a disjunction, the second is a conjunction

• The first is a conjunction, the second is a disjunction

• The first has no solution, the second has two solutions

• Both are solved the same way

How many solutions do you typically get when solving an absolute value equation?

• None

• Three

• Two

• One

Why does the equation 3x + 8 = 5 have no solution?

• Because the absolute value cannot equal a negative number

• Because 3x + 8 is always positive

• Because 3x + 8 cannot be negative

• Because the absolute value cannot be negative