Understanding Equivalent Equations

The video tutorial explains how to create equivalent equations by performing the same operations on both sides of an equation. Starting with x = -3, the tutorial demonstrates multiplying by 4, subtracting 5, dividing by 3, and adding 8 to both sides, resulting in equivalent equations. The final step involves verifying that x = -3 is a solution to all these equations, confirming their equivalence.

What is the definition of equivalent equations?

• Equations that have the exact same solution.

• Equations that have infinite solutions.

• Equations that have different solutions.

• Equations that have no solutions.

What is the first operation performed on the equation x = -3?

• Dividing by 3

• Adding 8

• Multiplying by 4

• Subtracting 5

After multiplying both sides of x = -3 by 4, what is the resulting equation?

• x = -3

• x = -12

• 4x = -3

• 4x = -12

What operation is performed after multiplying by 4?

• Adding 8

• Multiplying by 2

• Subtracting 5

• Dividing by 3

What is the equation after subtracting 5 from both sides of 4x = -12?

• 4x - 5 = -12

• 4x = -17

• 4x - 5 = -17

• x = -17

What is the next step after subtracting 5 from both sides?

• Dividing by 3

• Multiplying by 4

• Adding 8

• Subtracting 2

What is the equation after dividing both sides by 3?

• 4x - 5 / 3 = -17 / 3

• 4x = -17 / 3

• x = -17 / 3

• 4x - 5 = -17

What is the final operation performed on the equation?

• Subtracting 5

• Multiplying by 4

• Adding 8

• Dividing by 3

What is the final equivalent equation after all operations?

• 4x - 5 / 3 + 8 = 7/3

• 4x = 7/3

• 4x - 5 = 7/3

• x = 7/3

How is the solution x = -3 verified in the final equation?

• By using a calculator.

• By graphing the equation.

• By solving for x again.

• By substituting x = -3 and checking if both sides are equal.