Solving Absolute Value Equations: Part 2 Challenge

This video tutorial by Mr. Backer covers solving absolute value equations, starting with basic examples and progressing to more complex scenarios. It explains the process of isolating the absolute value, splitting equations, and solving for variables. The tutorial also addresses cases where no solution exists due to negative values and concludes with a final example to reinforce the concepts.

What is the first step in solving the equation |2x - 7| - 5 = 4?

• Add 5 to both sides

• Subtract 5 from both sides

• Multiply both sides by 2

• Divide both sides by 2

After isolating the absolute value in the equation |2x - 7| = 9, what are the two resulting equations?

• 2x - 7 = 9 and 2x + 7 = -9

• 2x + 7 = 9 and 2x + 7 = -9

• 2x + 7 = 9 and 2x - 7 = -9

• 2x - 7 = 9 and 2x - 7 = -9

In the equation 3|2x - 6| = 12, what is the first step to isolate the absolute value?

• Divide both sides by 3

• Multiply both sides by 3

• Add 3 to both sides

• Subtract 3 from both sides

What are the solutions for the equation |2x - 6| = 4?

• x = -5 and x = 1

• x = 5 and x = -1

• x = -5 and x = -1

• x = 5 and x = 1

In the equation 2|w| + 7 = 13, what is the first step to isolate the absolute value?

• Divide both sides by 2

• Subtract 7 from both sides

• Add 7 to both sides

• Multiply both sides by 2

What are the solutions for the equation |w| = 3?

• w = 3 and w = -3

• w = 3 and w = 0

• w = -3 and w = 0

• w = 3 and w = 1

Why does the equation |3x + 5| + 6 = 2 have no solution?

• Because the equation is not balanced

• Because the absolute value is not isolated

• Because the variable is on the right side

• Because the result is a negative number

What should you do if you encounter a negative result when solving an absolute value equation?

• Continue solving as usual

• Check if the absolute value is isolated

• Multiply both sides by -1

• Add a positive number to both sides

In the equation |3x + 5| - 6 = -2, what is the first step to isolate the absolute value?

• Subtract 6 from both sides

• Add 6 to both sides

• Divide both sides by 3

• Multiply both sides by 3

What are the solutions for the equation |3x + 5| = 4?

• x = -1/3 and x = -3

• x = 1/3 and x = 3

• x = 1/3 and x = -3

• x = -1/3 and x = 3