Understanding Linear Equations with Fractions

This video tutorial explains how to solve linear equations in one variable that involve fractions. It covers two methods: working with fractions directly or clearing them by multiplying both sides by the least common denominator (LCD). The tutorial provides step-by-step examples, demonstrating how to find the LCD, simplify fractions, and solve the equations. The first example uses denominators 6, 3, and 18, while the second example uses 3, 9, and 27. The video emphasizes simplifying fractions and solving for the variable.

What is the first step in solving linear equations with fractions?

• Divide both sides by the largest fraction

• Subtract fractions from both sides

• Multiply both sides by the least common denominator

• Add fractions on both sides

How do you determine the least common denominator?

• By dividing the largest denominator by the smallest

• By subtracting the smallest denominator from the largest

• By finding the smallest common multiple of all denominators

• By adding all denominators

What is the least common denominator for the numbers 6, 3, and 18?

• 36

• 6

• 9

• 18

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

• Add all terms to one side

• Simplify the equation by canceling common factors

• Multiply all terms by zero

• Divide all terms by the largest coefficient

What is the simplified solution for the first example equation?

• x = 1/11

• x = 11/1

• x = 45/11

• x = 11/45

In the second example, what is the least common denominator for 3, 9, and 27?

• 3

• 27

• 9

• 18

What is the result of multiplying 9 by 7x in the second example?

• 63x

• 16x

• 72x

• 27x

What is the final solution for the second example equation?

• x = -5/51

• x = 51/5

• x = -51/5

• x = 5/51

What operation is performed to get the X terms on the same side in the second example?

• Divide both sides by 12x

• Add 12x to both sides

• Multiply both sides by 12x

• Subtract 12x from both sides

What is the purpose of writing 27 as a fraction with a denominator of one?

• To add more fractions to the equation

• To simplify the multiplication process

• To make the equation more complex

• To divide the equation by 27