Solving Linear Equations with Fractions

This video tutorial explains how to solve linear equations with fractions by using the lowest common denominator (LCD) to eliminate fractions. The instructor provides three examples, demonstrating the process of multiplying all terms by the LCD, simplifying, and solving the resulting linear equations. The tutorial emphasizes the importance of maintaining balance by performing the same operations on both sides of the equation.

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

• Subtract all the fractions

• Add all the fractions

• Find the lowest common denominator (LCD)

• Find the common numerator

Why is it acceptable to multiply both sides of an equation by the LCD?

• Because it keeps the equation balanced

• Because it eliminates the variables

• Because it simplifies the equation

• Because it changes the equation

In the equation x/3 + x/8 = 11/24, what is the LCD?

• 3

• 8

• 24

• 11

After multiplying each term by the LCD in the equation x/3 + x/8 = 11/24, what is the simplified form of the left side?

• 8x + 3x

• 8x + 24x

• 3x + 24x

• 24x + 8x

In the equation 3x/4 - 3 = x/2 + 2, what is the LCD?

• 8

• 4

• 3

• 2

What is the result of multiplying each term by the LCD in the equation 3x/4 - 3 = x/2 + 2?

• 3x - 3 = 2x + 2

• 3x - 12 = x + 8

• 3x - 3 = x + 2

• 3x - 12 = 2x + 8

In the equation (x-3)/5 - 1 = (x-5)/4, what is the LCD?

• 4

• 20

• 5

• 1

What is the simplified form of the left side after multiplying by the LCD in the equation (x-3)/5 - 1 = (x-5)/4?

• 4(x-3) - 5

• 5(x-3) - 4

• 4(x-3) - 20

• 5(x-3) - 20

What is the next step after combining like terms in the equation (x-3)/5 - 1 = (x-5)/4?

• Divide by the coefficient of x

• Multiply by the LCD again

• Add the constants

• Eliminate the smaller x term

What is the final value of x in the equation (x-3)/5 - 1 = (x-5)/4?

• x = -7

• x = 7

• x = 20

• x = -20