Solving Equations for Variables

The video tutorial explains how to solve equations for variables U and x. It begins by isolating U in the equation U * (GX + C) = Y + H, using division to undo multiplication. Then, it focuses on solving for x by distributing U and isolating x through subtraction and division. Finally, it demonstrates how to express x in different forms by dividing each term in the numerator by the denominator.

What is the first step in solving an equation for a variable?

• Add a constant to both sides

• Isolate the variable on one side

• Multiply both sides by a constant

• Subtract a constant from both sides

How do you solve for U in the equation U * (GX + C) = Y + H?

• Subtract GX + C from both sides

• Divide both sides by GX + C

• Multiply both sides by GX + C

• Add GX + C to both sides

What is the purpose of dividing both sides of an equation by the same quantity?

• To isolate the variable

• To simplify the equation

• To eliminate the variable

• To add complexity to the equation

What operation is used to clear the parentheses when solving for X?

• Subtraction

• Addition

• Division

• Distribution

After distributing U, what is the next step to isolate the X term?

• Add CU to both sides

• Subtract CU from both sides

• Multiply both sides by CU

• Divide both sides by CU

Why is it common to write variables in alphabetical order when solving equations?

• It affects the product

• It is required by mathematical rules

• It is a common convention for clarity

• It simplifies the equation

What is the final operation to solve for X after isolating the X term?

• Add GU to both sides

• Divide both sides by GU

• Multiply both sides by GU

• Subtract GU from both sides

How can the expression for X be simplified further?

• By subtracting all terms in the numerator

• By multiplying all terms in the numerator

• By dividing each term in the numerator by the denominator

• By adding all terms in the numerator

What common factor allows further simplification of the expression for X?

• U

• G

• H

• C

Which of the following is a correct expression for X after simplification?

• X = Y / GU - H / GU - C / G

• X = Y / GU - H / GU + C / G

• X = Y / GU + H / GU - C / G

• X = Y / GU + H / GU + C / G