Verification and Solving for Variables

The video tutorial explains how to solve for variables in proportions using the concept that the product of the extremes must equal the product of the means, or that cross products must be equal. It provides a step-by-step guide to solving equations for variables X and Y, demonstrating the process of cross multiplication and division. The tutorial emphasizes the importance of verifying solutions by substituting values back into the original equation.

What is the principle used to solve for a variable in proportions?

• The ratio of the extremes to the means must be one

• The product of the extremes must equal the product of the means

• The difference between the extremes and means must be zero

• The sum of the extremes equals the sum of the means

In the first example, what operation is performed to isolate X?

• Adding 24 to both sides

• Multiplying both sides by 24

• Subtracting 24 from both sides

• Dividing both sides by 24

In the second example, what is the value of Y after solving the equation?

• 30

• 40

• 25

• 35

What is the first step in solving the second example for Y?

• Add the means and extremes

• Determine the product of the extremes

• Determine the product of the means

• Subtract the means from the extremes

Why is it important to verify the solution by substituting back into the original equation?

• To change the equation

• To find a different solution

• To simplify the equation further

• To ensure the solution is consistent with the equation

What should be the result when substituting Y back into the equation in the verification step?

• The left side should be less than the right side

• The left side should be zero

• The left side should be greater than the right side

• The left side should equal the right side