Understanding Equivalent Equations

The video tutorial explains how to create equivalent equations by applying operations to both sides of an equation. It provides two examples: starting with x = 9 and x = 5, and demonstrates operations such as addition, division, and subtraction to form new equations with the same solution. The tutorial emphasizes simplifying fractions and maintaining equivalent solutions throughout the process.

What is the purpose of performing the same operation on both sides of an equation?

• To eliminate variables

• To change the solution of the equation

• To maintain the equality of the equation

• To make the equation more complex

In the first example, what is the result of adding 5 to both sides of the equation x = 9?

• x = 9

• x + 5 = 14

• x = 14

• x + 5 = 9

What is the simplified form of 14 divided by 6?

• 3/7

• 2/3

• 14/6

• 7/3

How do you express 2 as a fraction with a denominator of 3?

• 2/3

• 6/3

• 3/2

• 1/3

What is the equivalent equation after subtracting 2 from both sides of the equation (x + 5)/6 = 7/3?

• (x + 5)/6 = 3/3

• (x + 5)/6 = 2/3

• (x + 5)/6 = 1/3

• (x + 5)/6 = 5/3

In the second example, what is the result of multiplying both sides of x = 5 by 8?

• x = 40

• 8x = 40

• 8x = 5

• x = 8

What is the second equivalent equation after adding 6 to both sides of 8x = 40?

• 8x + 6 = 46

• 8x + 6 = 40

• 8x = 46

• x + 6 = 46

What is the result of dividing both sides of 8x + 6 = 46 by 3?

• 8x/3 + 6 = 46/3

• (8x + 6)/3 = 15

• 8x + 6 = 15

• (8x + 6)/3 = 46/3

Why is it important to simplify fractions in equivalent equations?

• To make the equation more complex

• To change the solution of the equation

• To find a common denominator

• To make calculations easier and more accurate

What is the final equivalent equation in the second example?

• (8x + 6)/3 = 15

• (8x + 6)/3 = 46/3

• 8x + 6 = 46

• 8x = 46