Solving Absolute Value Equations: Isolate and Solve

The video tutorial explains how to solve absolute value equations by isolating the absolute value, setting up two equations, and solving them. It demonstrates the process with two examples, verifying solutions for accuracy. The tutorial emphasizes understanding the principle that absolute values can equal both positive and negative numbers, and encourages checking solutions.

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

• Subtract a constant from both sides

• Isolate the absolute value

• Add a constant to both sides

• Multiply both sides by a constant

After isolating the absolute value, what is the next step?

• Add the absolute value to both sides

• Multiply both sides by -1

• Check the solutions

• Set up and solve two equations

How do you set up the second equation when solving an absolute value equation?

• Keep the absolute value and change the sign of the constant

• Drop the absolute value and change the sign of the constant

• Add the absolute value to both sides

• Multiply both sides by -1

What are the solutions to the equation |x + 4| = 5?

• x = 5 and x = -5

• x = 9 and x = -1

• x = 1 and x = -9

• x = 1 and x = -1

How do you verify the solutions to an absolute value equation?

• By multiplying the solutions by -1

• By dividing the solutions by the constant

• By adding the solutions to both sides

• By substituting the solutions back into the original equation

What is the first step in solving the equation |3x - 1| - 9 = 4?

• Divide both sides by 3

• Subtract 9 from both sides

• Multiply both sides by 3

• Add 9 to both sides

What are the two equations derived from |3x - 1| = 13?

• 3x - 1 = 13 and 3x - 1 = -13

• 3x + 1 = 13 and 3x + 1 = -13

• 3x - 1 = 13 and 3x + 1 = 13

• 3x + 1 = 13 and 3x - 1 = 13

What is the solution to the equation 3x - 1 = 13?

• x = 4

• x = 7

• x = 5

• x = 6

What is the solution to the equation 3x - 1 = -13?

• x = -4

• x = -5

• x = -6

• x = -7

What are the solutions to the equation |3x - 1| = 13?

• x = 11/3 and x = -1

• x = 12/3 and x = -2

• x = 13/3 and x = -3

• x = 14/3 and x = -4