Solving Equations for Variables

The video tutorial demonstrates solving two algebraic equations for specified variables. The first equation involves isolating B1 in a = 12 * H * (B1 + B2) by eliminating fractions and rearranging terms. The second equation focuses on isolating Z in 3Z + x - y = 2x + 4 by systematically removing other variables and simplifying the expression. The tutorial emphasizes algebraic manipulation techniques such as multiplication, division, addition, and subtraction to achieve the solutions.

What is the main goal when solving an equation for a specified variable?

• To multiply all terms by zero

• To isolate the specified variable

• To eliminate all variables

• To add all terms together

In the equation a = 12 * H * (B1 + B2), what is the first step to solve for B1?

• Multiply by 1/2

• Divide by 12

• Subtract H from both sides

• Add B2 to both sides

How can fractions be removed from an equation?

• By subtracting fractions

• By dividing by zero

• By multiplying to eliminate the fraction

• By adding fractions

What operation is used to simplify the equation by removing H?

• Multiplication

• Division

• Subtraction

• Addition

After dividing by H, what is the next step to isolate B1?

• Divide by B2

• Add B2 to both sides

• Multiply by B2

• Subtract B2 from both sides

What is the final form of B1 after solving the equation?

• B1 = 2aH + B2

• B1 = 2aH / B2

• B1 = 2aH - B2

• B1 = 2aH * B2

What is the purpose of distributing a positive one in front of (B1 + B2)?

• To simplify the expression

• To change the sign of B1

• To add B1 and B2

• To eliminate B2

What happens to the equation when you subtract B2 from both sides?

• B2 is added to both sides

• B2 is eliminated from the equation

• B2 is multiplied by both sides

• B2 is divided by both sides

What is the effect of multiplying both sides of an equation by the same number?

• It keeps the equation balanced

• It changes the solution

• It eliminates variables

• It adds variables

In the equation 3Z + x - y = 2x + 4, what is the first step to solve for Z?

• Add y to both sides

• Divide by 3

• Subtract x from both sides

• Multiply by 3