Solving Equations with Fractions

The video tutorial guides viewers through solving an equation for x, starting with removing x from the denominator by multiplying both sides by nine minus x. It emphasizes the importance of setting conditions to avoid division by zero. The instructor then performs algebraic manipulations to isolate x, resulting in x equals three. The solution is verified to ensure it doesn't make the original equation undefined.

What is the first step suggested to solve the equation x + 1/(9-x) = 2/3?

• Add 1 to both sides

• Multiply both sides by 9-x

• Divide both sides by 2/3

• Subtract 1 from both sides

Why is it important to note that x cannot be equal to 9?

• Because it would make the numerator zero

• Because it would result in a negative number

• Because it would make the equation too complex

• Because it would make the denominator zero

What happens to the left-hand side of the equation after multiplying by 9-x?

• It becomes x + 1

• It becomes 2/3

• It becomes 9x

• It becomes zero

How do you combine the terms 3/3 x and 2/3 x?

• By dividing them to get 1/2 x

• By subtracting them to get 1/3 x

• By adding them to get 5/3 x

• By multiplying them to get 6/9 x

What is the reciprocal of 5/3 used for in the equation?

• To subtract from both sides

• To divide both sides

• To add to both sides

• To multiply both sides

What is the final value of x after solving the equation?

• x = 5

• x = 3

• x = 9

• x = 0

What is the purpose of multiplying by the reciprocal of 5/3?

• To add a fraction

• To eliminate the fraction

• To divide the fraction

• To create a new fraction

Why is it necessary to verify the solution x = 3?

• To see if it is greater than 9

• To confirm it is a negative number

• To ensure it doesn't make the denominator zero

• To check if it makes the numerator zero

What would happen if the solution was x = 9?

• It would make the equation negative

• It would make the equation zero

• It would make the equation undefined

• It would be a valid solution

What is the significance of the solution x = 3 in the context of the original equation?

• It makes the equation undefined

• It satisfies the equation without making the denominator zero

• It is greater than 9

• It is less than 0