Solving Equations with Variables

The video provides an algebra review with three worked examples, one of which is solved twice. It covers solving for variables in equations, focusing on handling unknowns in denominators. The video explains the correct and incorrect methods for solving equations, emphasizing the importance of algebraic operations. It also discusses solving physics equations with subscripts and squares, highlighting the need for careful handling of mathematical operations. The tutorial concludes with solving a complex equation, demonstrating step-by-step methods to isolate the desired variable.

What is the first step in solving the equation v = d/t when the unknown is in the denominator?

• Multiply both sides by the denominator

• Divide both sides by the numerator

• Add the unknown to both sides

• Subtract the unknown from both sides

Why is it incorrect to multiply both sides by 'd' when solving v = d/t for 't'?

• It simplifies the equation correctly

• It cancels out the unknown

• It assumes 1/t magically becomes t

• It results in a quadratic equation

In the equation vf^2 = vi^2 + 2ad, what do the subscripts 'f' and 'i' indicate?

• They indicate the same velocity

• They are coefficients

• They are constants

• They represent different velocities

What is the correct method to isolate 'a' in the equation vf^2 = vi^2 + 2ad?

• Add vi^2 to both sides

• Multiply both sides by 2d

• Subtract vi^2 from both sides

• Divide both sides by vf^2

How do you solve for 'vi' in the equation vf^2 = vi^2 + 2ad?

• Subtract vf^2 from both sides

• Add 2ad to both sides

• Take the square root of both sides

• Multiply both sides by vf^2

What is the first step in solving a complex equation with the unknown in the denominator?

• Multiply both sides by the entire denominator

• Divide both sides by the numerator

• Add the unknown to both sides

• Subtract the unknown from both sides

In solving for vs, why is it necessary to multiply by -1 at the end?

• To simplify the equation

• To eliminate the negative sign

• To add a constant

• To balance the equation

What does the subscript 's' in vs indicate in the context of the equation?

• It is a coefficient

• It is a constant

• It represents a specific velocity

• It indicates a sum

When solving for vs, what operation is performed after removing the unknown from the denominator?

• Multiply by the numerator

• Divide by the coefficient of the unknown

• Add the numerator to both sides

• Subtract the numerator from both sides

What is the final step in solving for vs in the given complex equation?

• Subtract the numerator from both sides

• Multiply by the entire denominator

• Add a constant to both sides

• Multiply by -1 to change the sign