Solving Equations and Variable Isolation

This video tutorial explains how to solve a multi-step equation involving fractions. It begins by introducing the concept of finding the value of x that satisfies the equation. The tutorial then demonstrates how to clear fractions by multiplying both sides by a common denominator. Next, it shows how to simplify the equation and isolate the variable x through addition and subtraction. Finally, the solution is verified by substituting the value back into the original equation to ensure both sides are equal.

What is the primary goal when solving an equation?

• To eliminate all variables

• To simplify the equation to zero

• To make both sides of the equation equal

• To find the value of y

What is the first step in clearing fractions from an equation?

• Add fractions to both sides

• Divide both sides by a common denominator

• Multiply both sides by a common denominator

• Subtract fractions from both sides

Why do we multiply both sides of the equation by 4 in this example?

• To add fractions

• To eliminate the variable

• To clear the fractions

• To simplify the equation

What operation is used to combine like terms on both sides of the equation?

• Addition

• Subtraction

• Multiplication

• Division

What is the result of adding 2x to both sides of the equation?

• The variable terms are eliminated

• The variable terms are combined on one side

• The equation becomes unsolvable

• The equation is simplified to zero

What is the next step after isolating the variable term 5x?

• Subtract 5 from both sides

• Divide both sides by 5

• Multiply both sides by 5

• Add 5 to both sides

What does dividing both sides by 5 achieve in the equation?

• It adds fractions to the equation

• It eliminates the variable

• It simplifies the equation to zero

• It isolates the variable

What is the solution to the equation after performing all operations?

• x = 10

• x = 8

• x = 0

• x = 5

How do we verify the solution to the equation?

• By substituting the value back into the equation

• By multiplying the solution by the variable

• By dividing the solution by the variable

• By adding the solution to both sides

What is the result when substituting x = 8 back into the original equation?

• Both sides equal zero

• Both sides equal eight

• Both sides equal four

• Both sides equal sixteen