Solving Linear Equations with Fractions

The video tutorial demonstrates solving an equation for x by simplifying fractions, isolating the variable, and verifying the solution. It begins with the problem statement, followed by clearing fractions using the least common multiple. The instructor then isolates x by performing algebraic operations and verifies the solution by substituting it back into the original equation.

What is the initial equation given in the problem?

• x - 8 = x/3 + 1/6

• x + 8 = x/2 - 1/3

• x + 8 = x/3 - 1/6

• x - 8 = x/2 + 1/3

What is the least common multiple of the denominators in the equation?

• 12

• 3

• 9

• 6

After clearing the fractions, what does the equation become?

• 6x - 48 = 3x + 1

• 6x + 48 = 3x - 1

• 6x - 48 = 2x + 1

• 6x + 48 = 2x - 1

What operation is performed to isolate x on one side of the equation?

• Add 2x to both sides

• Subtract 2x from both sides

• Multiply both sides by 2

• Divide both sides by 2

What is the value of x after solving the equation?

• 49/2

• 49/3

• 49/4

• 49/5

What is the final step to solve for x in the equation 4x = 49?

• Multiply both sides by 4

• Divide both sides by 4

• Add 4 to both sides

• Subtract 4 from both sides

How do you verify the solution x = 49/4?

• Check if x = 49/4 satisfies any equation

• Substitute x = 49/4 into a different equation

• No verification is needed

• Substitute x = 49/4 into the original equation

What is the result of substituting x = 49/4 back into the original equation?

• The left side equals the right side

• The left side is greater than the right side

• The left side is less than the right side

• The equation becomes undefined

What is the purpose of multiplying both sides of the equation by 6 during verification?

• To introduce new fractions

• To simplify the fractions

• To eliminate the variable

• To change the equation

What is the simplified form of 3 times 49 over 2?

• 147/2

• 147/3

• 147/4

• 147/5