Understanding Double Absolute Value Equations

The video tutorial explains how to solve a double absolute value equation, specifically |x + 3| = |2x - 3|. The instructor discusses the conditions under which the absolute values are equal and solves two separate equations: x + 3 = 2x - 3 and x + 3 = -(2x - 3). The solutions x = 6 and x = 0 are verified by substituting back into the original equation. The tutorial concludes with a challenge to consider the equation as an inequality.

What are the two conditions that make the absolute values of two expressions equal?

• Both expressions are positive.

• Both expressions are negative.

• The expressions are equal or negatives of each other.

• The expressions are both zero.

What is the first step in solving the equation |x + 3| = |2x - 3|?

• Subtract x from both sides.

• Add 3 to both sides.

• Set x + 3 equal to 2x - 3.

• Multiply both sides by 2.

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

• x = -6

• x = 3

• x = 6

• x = -3

How do you solve the equation x + 30 = -2x + 30?

• Divide both sides by 3.

• Multiply both sides by -1.

• Subtract 30 from both sides.

• Add 2x to both sides.

What is the solution to the equation 3x = 0?

• x = 3

• x = 0

• x = -3

• x = 1

Why is it important to verify solutions in the original equation?

• To confirm the solutions satisfy the original conditions.

• To simplify the equation further.

• To ensure the solutions are positive.

• To find additional solutions.

What is the absolute value of 9?

• 0

• -9

• 9

• 18

What is the absolute value of -30?

• -60

• 30

• 0

• -30

What happens if the equality sign in the equation is replaced with an inequality?

• The solutions need to be re-evaluated.

• The equation becomes unsolvable.

• The equation becomes a quadratic equation.

• The solutions remain the same.

What should you do if the equation becomes an inequality?

• Consider the inequality conditions.

• Solve it as if it were an equality.

• Ignore the inequality.

• Multiply both sides by zero.