Solving Linear Equations and Fractions

The video tutorial explains how to solve a linear equation in one variable, focusing on two methods: solving with fractions and clearing fractions first. The instructor demonstrates both approaches, emphasizing the importance of finding a common denominator and using reciprocal multiplication. The solution to the equation is y = 15/14, and the video concludes with a summary of the methods used.

What is the first step in solving a linear equation in one variable?

• Isolate the variable on one side

• Multiply both sides by zero

• Add a constant to both sides

• Divide by the variable

What is the least common denominator for the fractions 1/5 and 1/2?

• 20

• 15

• 10

• 5

What is the purpose of finding a common denominator in an equation with fractions?

• To change the equation to a quadratic form

• To eliminate the variable

• To simplify the addition or subtraction of fractions

• To make the equation more complex

How do you solve for y in the equation 7/10y = 3/4?

• Multiply both sides by 7/10

• Divide both sides by 3/4

• Multiply both sides by 10/7

• Add 10/7 to both sides

What is the result of multiplying 10/7 by 7/10?

• 10

• 1

• 7

• 0

What is the least common denominator for the fractions 1/5, 1/2, and 3/4?

• 20

• 15

• 25

• 10

What operation is used to clear fractions from an equation?

• Division

• Addition

• Subtraction

• Multiplication

After clearing fractions, what is the simplified form of 20 times y over 5?

• 5y

• 20y

• 4y

• 10y

What is the final solution for y in the equation after clearing fractions?

• y = 1

• y = 14/15

• y = 15/14

• y = 0

What is the final step in solving a linear equation after clearing fractions?

• Divide by the coefficient of the variable

• Multiply by zero

• Subtract the variable from both sides

• Add a constant to both sides