Solving Equations with Fractions

The video tutorial explains how to solve the equation nine-fourths x equals negative nine using two methods. The first method involves using the reciprocal to isolate x, while the second method clears fractions by multiplying both sides by the least common denominator. Both methods arrive at the solution x equals negative four. The tutorial concludes with a verification step to ensure the solution is correct.

What is the first step in solving the equation nine-fourths x equals negative nine?

• Multiply both sides by nine

• Isolate the variable x

• Subtract four from both sides

• Add nine to both sides

What operation is used to solve the equation using the reciprocal method?

• Subtraction

• Addition

• Multiplication

• Division

Why do we multiply by the reciprocal instead of dividing by a fraction?

• It avoids complex numbers

• It is easier to calculate

• It is a standard rule in mathematics

• It simplifies the equation

What is the result of multiplying nine-fourths by its reciprocal?

• Zero

• One

• Negative one

• Nine

What is the least common denominator used in the second method?

• Nine

• Four

• One

• Thirty-six

What is the result of clearing fractions by multiplying both sides by four?

• Nine x equals negative nine

• Nine x equals negative thirty-six

• Four x equals negative nine

• Four x equals negative thirty-six

How do you verify the solution to the equation?

• By asking a teacher

• By using a calculator

• By solving a different equation

• By checking if the solution satisfies the original equation

What is the final solution for x in the equation nine-fourths x equals negative nine?

• x equals negative nine

• x equals negative four

• x equals four

• x equals nine

What is the purpose of writing negative four as a fraction with a denominator of one?

• To convert it to a decimal

• To simplify the equation

• To make it easier to multiply

• To find a common factor

What does the product of nine times negative one equal?

• Negative nine

• Positive nine

• Negative one

• Zero