Solving Absolute Value Equations Challenge

The video tutorial explains how to solve absolute value equations, starting with a definition of absolute value as the distance from zero on a number line. It covers the concept of having two solutions for non-zero absolute values and provides a step-by-step guide to solving these equations. The tutorial includes examples, case analysis, and the use of set notation to present solutions. It also touches on special cases that will be explored in a subsequent video.

What is the definition of an absolute value?

• The distance from 0 on a number line

• The product of a number and its reciprocal

• The sum of all positive numbers

• The difference between a number and zero

If the absolute value of x equals 5, what are the possible values of x?

• 0 and -5

• 0 and 5

• 5 and 10

• 5 and -5

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

• Multiply both sides by 2

• Subtract 4 from both sides

• Add 5 to both sides

• Isolate the absolute value expression

In the equation |x + 4| = 10, what are the two cases to consider?

• x + 4 = 10 and x + 4 = 4

• x + 4 = 10 and x + 4 = 14

• x + 4 = 10 and x + 4 = 0

• x + 4 = 10 and x + 4 = -10

What should you do if the absolute value expression is not isolated?

• Take the square root of both sides

• Divide both sides by 2

• Add or subtract terms to isolate it

• Multiply both sides by 2

In the equation |2x + 5| = 23, what is the solution for x?

• x = 9 or x = -14

• x = 18 or x = 28

• x = 9 or x = 14

• x = 18 or x = -28

What happens if the value inside the absolute value is negative?

• You need to continue isolating the absolute value

• The equation is already solved

• The equation has no solution

• You can ignore the negative sign

In the equation |x + 5| = -9, what can be concluded?

• x = 4

• There is no solution

• x = 9

• x = -14

How do you handle absolute value equations involving fractions?

• Add the numerator to both sides

• Multiply both sides by the denominator

• Subtract the numerator from both sides

• Treat the fraction as a quantity and isolate the absolute value

In the equation |x - 7| / 2 = 8, what is the solution for x?

• x = 7 or x = -7

• x = 23 or x = -9

• x = 16 or x = -16

• x = 8 or x = -8