Solving Absolute Value Equations

This video tutorial explains how to solve absolute value equations. It begins with a basic example where the absolute value is isolated on one side of the equation. The tutorial then progresses to more complex examples where absolute values appear on both sides of the equation. The video also covers scenarios where absolute value equations have no solution, emphasizing that absolute values cannot be negative. The tutorial aims to provide a comprehensive understanding of solving absolute value equations through step-by-step examples.

What is the first step in solving the equation |x - 2| + 6 = 10?

• Add 6 to both sides

• Subtract 6 from both sides

• Multiply both sides by 6

• Divide both sides by 6

Why do we consider both positive and negative values inside the absolute value?

• Because absolute values can be either positive or negative

• Because absolute values are always positive

• Because absolute values can be zero

• Because absolute values can be negative

What are the solutions to the equation |x - 2| = 4?

• x = 4 or x = -4

• x = 6 or x = 2

• x = 6 or x = -2

• x = 2 or x = -2

In the equation |x + 6| = |2x - 3|, what is the first step after removing the absolute values?

• Set the inside of the absolute values equal to each other

• Multiply both sides by 2

• Subtract 6 from both sides

• Add 6 to both sides

What is the solution to the equation x + 6 = 2x - 3?

• x = 9

• x = -9

• x = 3

• x = -3

What is the solution to the equation x + 6 = -2x - 3?

• x = 3

• x = -3

• x = -1

• x = 1

What is the final step in solving the equation x + 6 = 2x - 3?

• Divide both sides by 2

• Add 6 to both sides

• Subtract x from both sides

• Multiply both sides by 3

What is the final step in solving the equation x + 6 = -2x - 3?

• Add 2x to both sides

• Subtract 6 from both sides

• Divide both sides by 3

• Multiply both sides by 2

Why does the equation |x + 5| = -7 have no solution?

• Because absolute values can only be zero

• Because x cannot be positive

• Because absolute values cannot be negative

• Because x cannot be negative

What is the reason that |x - 2| = -3 has no solution?

• Because absolute values can only be zero

• Because absolute values cannot be negative

• Because x cannot be negative

• Because x cannot be positive