Solving Linear Equations and Fractions

This video tutorial covers solving two-step equations involving fractions. It begins with an introduction to the concept and the goal of isolating the variable. The video then provides four detailed examples, each demonstrating the process of solving equations step-by-step, including finding common denominators and converting improper fractions to mixed numbers. The tutorial emphasizes the importance of performing the same operation on both sides of the equation to maintain equality.

What is the primary goal when solving a two-step linear equation?

• To eliminate all fractions

• To isolate the variable on one side

• To multiply both sides by zero

• To add the same number to both sides

In the first example, what operation is performed to eliminate the fraction 1/4?

• Divide both sides by 1/4

• Subtract 1/4 from both sides

• Multiply both sides by 4

• Add 1/4 to both sides

What is the solution to the equation 2X + 1/4 = 3/5 after simplification?

• X = 7/20

• X = 7/40

• X = 1/2

• X = 3/5

In the second example, what is the common denominator used to add fractions?

• 15

• 10

• 5

• 20

What is the mixed number equivalent of the improper fraction 11/4?

• 3 3/4

• 3 1/4

• 2 3/4

• 2 1/4

In the third example, what operation is used to eliminate the term -5?

• Divide both sides by 5

• Subtract 5 from both sides

• Add 5 to both sides

• Multiply both sides by 5

What is the solution to the equation 1/4 = 3/5X - 5 after simplification?

• X = 5/3

• X = 8 3/4

• X = 7/4

• X = 35/4

In the fourth example, what is the first step to solve the equation 5 x 2 + 1 = 11/5?

• Multiply both sides by 3

• Subtract 2/3 from both sides

• Divide both sides by 5

• Add 2/3 to both sides

What is the improper fraction equivalent of the mixed number 2 and 13/15?

• 33/15

• 23/15

• 28/15

• 43/15

What is the final solution to the equation 2/3 - 1/2X = 11/5 after simplification?

• X = -43/15

• X = 43/15

• X = -23/15

• X = 23/15