Understanding Equivalent Equations

The video tutorial explains how to create equivalent equations using operations on given variables. It covers two examples: starting with x = 5 and x = 2, applying operations like subtraction, multiplication, division, and addition to form new equations with the same solutions. The tutorial emphasizes maintaining equality and simplifying fractions where applicable.

What is the purpose of creating equivalent equations?

• To simplify the equation

• To maintain the same solution while changing the equation's form

• To find different solutions for the same equation

• To make the equation more complex

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

• x - 9 = 9

• x - 9 = 14

• x - 9 = -4

• x - 9 = 0

After multiplying both sides of the equation x - 9 = -4 by 8, what is the new equation?

• 8(x - 9) = 32

• 8(x - 9) = -32

• x - 9 = -32

• x - 9 = 32

What is the final equivalent equation after adding 4 to both sides of 8(x - 9) = -32?

• 8(x - 9) + 4 = -36

• 8(x - 9) + 4 = 28

• 8(x - 9) + 4 = -28

• 8(x - 9) + 4 = 36

In the second example, what is the simplified form of the fraction 2/6?

• 1/6

• 2/3

• 1/3

• 1/2

What is the result of adding 8 to both sides of the equation x/6 = 1/3?

• x/6 + 8 = 25/3

• x/6 + 8 = 8/3

• x/6 + 8 = 1/3

• x/6 + 8 = 9/3

What is the final equivalent equation after multiplying both sides of x/6 + 8 = 25/3 by -3?

• -3(x/6 + 8) = -25

• -3(x/6 + 8) = 25

• -3(x/6 + 8) = 0

• -3(x/6 + 8) = 75