Solving Equations with Fractions

The video tutorial explains how to solve the equation 12y + 7 = 1/8y by isolating the variable y. It discusses the decision to solve the equation with fractions intact and demonstrates the process of eliminating y terms from both sides. The tutorial covers finding a common denominator to combine y terms, isolating y by subtracting and dividing, and verifying the solution through substitution. The solution is confirmed to be correct by checking both sides of the equation.

What is the first step in solving the equation 12y + 7 = 1/8y?

• Multiply both sides by 8

• Isolate y on one side

• Add 7 to both sides

• Subtract 1/8y from both sides

Why might one choose to keep fractions in the equation rather than eliminate them?

• It simplifies the process

• It is a personal preference

• It makes the equation longer

• It avoids additional calculations

What operation is performed to eliminate 1/8y from the right side of the equation?

• Add 1/8y to both sides

• Subtract 1/8y from both sides

• Divide both sides by 8

• Multiply both sides by 8

What is the least common denominator used to combine the y terms?

• 2

• 4

• 6

• 8

After simplifying, what is the equation before isolating y?

• 38y + 7 = 0

• 48y + 7 = 0

• 12y + 7 = 1/8y

• 38y = -7

What is the final step to solve for y in the equation 38y = -7?

• Add 7 to both sides

• Multiply both sides by the reciprocal of 38

• Multiply both sides by 38

• Divide both sides by 38

What is the solution for y in the equation 38y = -7?

• -56/3

• -7/38

• -7/3

• -38/7

How is the solution verified in the original equation?

• By substituting y back into the equation

• By multiplying both sides by 8

• By adding 7 to both sides

• By dividing both sides by 3

What is the result of substituting the solution back into the original equation?

• The left side equals 0

• The right side equals 0

• Both sides equal 7/3

• Both sides equal -7/3

What is the purpose of verifying the solution?

• To find a different solution

• To confirm both sides of the equation are equal

• To ensure the solution is in simplest form

• To check for calculation errors