Solving Equations with Fractions

The video tutorial demonstrates solving an equation involving the variable x by clearing fractions using the least common denominator, which is 16 in this case. The instructor multiplies both sides of the equation by 16, distributes it across terms, and performs cross-cancelling to eliminate denominators. The equation is simplified to contain only integers, and then solved using the Addition and Multiplication Properties of Equality, resulting in x equaling negative 4.

What is the first step in solving an equation involving fractions?

• Subtract the smallest term

• Divide by the largest coefficient

• Add all terms together

• Clear the fractions

What is the least common denominator used in this problem?

• 16

• 24

• 12

• 8

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

• To make the equation longer

• To simplify the constants

• To eliminate fractions

• To add more variables

What is the purpose of distributing the multiplier across terms?

• To increase the number of terms

• To simplify the equation

• To ensure each term is multiplied

• To eliminate variables

What does cross-cancelling help achieve in the equation?

• It changes the variable

• It eliminates denominators

• It adds more fractions

• It increases the coefficients

After distributing and cross-cancelling, what type of equation do we have?

• An equation with integers

• An equation with decimals

• An equation with variables only

• An equation with fractions

What is the result of combining like terms 14x and -11x?

• 0x

• 3x

• 14x

• 25x

Which property is used to eliminate the constant term?

• Division Property of Equality

• Multiplication Property of Equality

• Addition Property of Equality

• Subtraction Property of Equality

What operation is performed to isolate the variable term 3x?

• Multiply both sides by 3

• Subtract 16 from both sides

• Divide both sides by 3

• Add 16 to both sides

What does the equation become after subtracting 16 from both sides?

• 3x = 16

• 3x = 4

• 3x = -12

• 3x = 0