Solving Equations and Fractions

The video tutorial explains how to solve a radical equation by substituting a given value for f(x), isolating the square root, and solving for x. The process involves performing arithmetic operations to simplify the equation, squaring both sides to eliminate the square root, and verifying the solution by substituting back into the original equation. The tutorial provides a step-by-step approach to ensure the solution is correct.

What is the first step in solving the equation f(x) = 8 for the given function?

• Multiply both sides by 6

• Add 2 to both sides

• Substitute 8 for f(x) and solve the resulting equation

• Subtract 3 from both sides

After substituting 8 for f(x), what operation is performed to isolate the square root?

• Add 3 to both sides

• Divide both sides by 6

• Subtract 3 from both sides

• Multiply both sides by 6

What is the result of dividing both sides by 6 in the equation 11 = 6√(x-2)?

• 11/6 = 6x

• 11/6 = x-2

• 11/6 = √(x-2)

• 11/6 = x

What is the purpose of squaring both sides of the equation 11/6 = √(x-2)?

• To simplify the fraction

• To isolate x

• To eliminate the square root

• To find a common denominator

What is the result of squaring 11/6?

• 121/6

• 11/36

• 11/12

• 121/36

Why do we need to find a common denominator when solving for x?

• To multiply fractions

• To simplify the equation

• To add fractions correctly

• To divide fractions

What is the least common denominator used in the solution?

• 48

• 24

• 12

• 36

What is the final value of x after solving the equation?

• 121/36

• 193/36

• 72/36

• 11/6

What is the purpose of substituting the solution back into the original equation?

• To find a new solution

• To check for calculation errors

• To verify the solution is correct

• To simplify the equation

What is the result of verifying the solution by substitution?

• The solution is incorrect

• The solution needs adjustment

• The solution is correct

• The solution is incomplete