Understanding Absolute Value Equations

In this video, Mr. J explains how to solve absolute value equations with variables on both sides. The process involves isolating the absolute value, setting up two equations (one positive and one negative), and solving each equation separately. The solutions are then verified by substituting them back into the original equation. The video provides a step-by-step guide to ensure understanding and accuracy in solving these types of equations.

What is the first step in solving an absolute value equation with variables on both sides?

• Add constants to both sides

• Combine like terms

• Isolate the absolute value

• Distribute the negative sign

When writing two equations from an absolute value equation, what should one of the equations be equal to?

• The original equation

• A negative number

• Zero

• A positive number

In the equation 3x - 1 = x + 13, what is the result after subtracting x from both sides?

• 2x = 12

• x - 1 = 13

• 3x = 14

• 2x - 1 = 13

What operation is used to isolate x in the equation 2x = 14?

• Division

• Multiplication

• Subtraction

• Addition

What is the first step in solving the negative equation 3x - 1 = -x - 13?

• Subtract x from both sides

• Distribute the negative sign

• Multiply both sides by -1

• Add 1 to both sides

After distributing the negative sign in the equation 3x - 1 = -x - 13, what is the next step?

• Divide by 4

• Subtract 1 from both sides

• Multiply by 2

• Add x to both sides

What is the solution for x in the equation 4x = -12?

• x = -4

• x = 4

• x = -3

• x = 3

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

• By graphing the equation

• By substituting the solutions back into the original equation

• By solving a different equation

• By checking the solutions with a calculator

What is the absolute value of -10?

• -10

• 20

• 10

• 0

What are the two solutions for the equation 3x - 1 = x + 13?

• x = 7 and x = -3

• x = -7 and x = -3

• x = 7 and x = 3

• x = -7 and x = 3