Solving Equations with Reciprocals

The video tutorial demonstrates two methods to solve the equation 2/3x = -6. The traditional method involves dividing both sides by the coefficient of x, resulting in x = -9. An alternative one-step method uses the reciprocal of the coefficient to simplify the equation directly, also yielding x = -9. Both methods emphasize the use of reciprocals in solving equations involving fractions.

What equation are we trying to solve in this tutorial?

• 3/2x = -6

• 2/3x = -6

• 3/2x = 6

• 2/3x = 6

What is the first step in the traditional method to solve 2/3x = -6?

• Multiply both sides by 2/3

• Add 6 to both sides

• Divide both sides by 2/3

• Subtract 2/3 from both sides

When dividing by a fraction, what operation can you use instead?

• Division by the reciprocal

• Multiplication by the reciprocal

• Addition of the fraction

• Subtraction of the fraction

What is the result of solving the equation using the traditional method?

• x = 3

• x = -3

• x = 9

• x = -9

What is the alternative method introduced to solve the equation?

• Multiplying both sides by the reciprocal

• Subtracting the reciprocal from both sides

• Dividing both sides by the reciprocal

• Adding the reciprocal to both sides

In the alternative method, what happens when you multiply both sides by the reciprocal?

• The solution becomes positive

• The equation remains unchanged

• The coefficients cancel out

• The equation becomes more complex

What is the final solution using the alternative method?

• x = 9

• x = -3

• x = 3

• x = -9