Solving Equations with Fractions

The video tutorial explains how to solve the equation 12y + 7 = 1/8y by clearing fractions using the least common denominator. It demonstrates simplifying the equation, isolating the variable y, and solving for y. The solution is verified by substituting back into the original equation to ensure both sides are equal.

What is the main goal when solving the equation 12y + 7 = 1/18y?

• To simplify the equation to zero

• To find the value of y that makes both sides equal

• To eliminate all fractions

• To find the least common denominator

Why do we multiply both sides of the equation by the least common denominator?

• To make the equation more complex

• To clear the fractions from the equation

• To add more fractions

• To change the equation completely

What is the least common denominator used in the equation 12y + 7 = 1/8y?

• 8

• 4

• 2

• 16

After clearing fractions, what is the next step in solving the equation?

• Add more fractions

• Multiply by another number

• Distribute and simplify the equation

• Divide by the least common denominator

What operation is used to eliminate y from the right side of the equation?

• Addition

• Division

• Multiplication

• Subtraction

What is the result of subtracting y from both sides of the equation?

• y + 56 = 0

• 0 = 0

• 4y + 56 = 0

• 3y + 56 = 0

How do you isolate y in the equation 3y + 56 = 0?

• Add 56 to both sides

• Divide both sides by 3

• Multiply both sides by 3

• Subtract 56 from both sides

What is the final solution for y in the equation?

• y = -56/3

• y = 0

• y = 56

• y = -56

Why is it important to verify the solution by substituting back into the original equation?

• To ensure the solution is correct

• To make the equation more complex

• To find a new solution

• To change the solution

What should both sides of the equation equal after substituting the solution back?

• 56

• 1

• 0

• -7/3