Solving Linear Equations and Fractions

The video tutorial explains how to solve a linear equation with fractions in one variable. It demonstrates two methods: solving directly and solving by first clearing fractions. The tutorial provides a detailed step-by-step process for each method, ensuring the same solution is reached. It concludes with verifying the solution by substituting the value back into the original equation.

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

• Add fractions to both sides

• Subtract the variable from both sides

• Isolate the variable on one side

• Multiply both sides by the variable

Why might you multiply both sides of an equation by the least common denominator?

• To increase the number of fractions

• To make the equation more complex

• To clear fractions from the equation

• To change the variable

What is the least common denominator used to add 1/2 and 1/6?

• 2

• 3

• 6

• 12

What is the reciprocal of 3/4?

• 4/3

• 3/4

• 1/3

• 3/2

What is the solution to the equation 3/4 X - 1/6 = 1/2?

• X = 3/4

• X = 8/9

• X = 2/3

• X = 1/2

What is the simplified form of 3/6?

• 2/3

• 1/2

• 1/3

• 3/2

What is the least common denominator of 4, 6, and 2?

• 6

• 12

• 8

• 10

After clearing fractions, what is the equation simplified to before solving for X?

• 9X = 8

• X = 8/9

• 3X = 4

• 6X = 9

What operation is used to verify the solution of an equation?

• Multiplication

• Substitution

• Division

• Addition

What is the result of substituting X = 8/9 back into the original equation?

• 3/4 = 1/2

• 1/2 = 1/2

• 1/3 = 1/2

• 2/3 = 1/2