Solving Absolute Value Equations Challenge

The video tutorial introduces the concept of absolute value, explaining it as the distance from zero on a number line. It covers solving absolute value equations, starting with basic examples and progressing to more complex problems. The tutorial emphasizes the importance of isolating the absolute value sign before solving and provides step-by-step solutions to various equations. The video concludes with practice problems for viewers to solve.

What is the absolute value of -5?

• -5

• 0

• 5

• 10

If the absolute value of x is 6, what are the possible values of x?

• 6 and -6

• 6 and 12

• 6 and 0

• 6 and -12

What are the solutions to the equation |x| = 19?

• 19 and 0

• 19 and 1

• 19 and -19

• 19 and -1

Why can't the absolute value of a number be negative?

• Because it represents distance

• Because it represents direction

• Because it represents magnitude

• Because it represents position

What is the first step in solving the equation |x - 5| = 1?

• Multiply both sides by 5

• Subtract 5 from both sides

• Add 5 to both sides

• Divide both sides by 5

What should you do after isolating the absolute value sign in an equation?

• Divide both sides by 2

• Multiply both sides by -1

• Add the same number to both sides

• Split the equation into two cases

In the equation |2x + 5| = 31, what are the two resulting equations after splitting?

• 2x + 5 = 31 and 2x + 5 = -31

• 2x + 5 = 31 and 2x + 5 = 0

• 2x + 5 = 31 and 2x + 5 = 1

• 2x + 5 = 31 and 2x + 5 = 5

What is the solution to the equation 2x + 5 = 31?

• x = -13

• x = 13

• x = -18

• x = 18

What is the solution to the equation 2x + 5 = -31?

• x = -13

• x = -18

• x = 18

• x = 13

What are the final solutions to the equation |2x + 5| = 31?

• x = -13 and x = 18

• x = -13 and x = -18

• x = 13 and x = 18

• x = 13 and x = -18