Rational Equations and Validity Checks

This video tutorial guides viewers through solving a rational equation. It covers identifying restrictions, finding the least common denominator (LCD), multiplying the equation by the LCD, simplifying the equation, solving for x, and verifying the solution. The tutorial emphasizes avoiding values that make denominators zero and checking the solution against these restrictions.

What is the first step in solving a rational equation?

• Finding the LCD

• Identifying restrictions

• Multiplying by the LCD

• Checking the solution

Why do we need to find restrictions in a rational equation?

• To avoid solutions that make the denominator zero

• To find the LCD

• To check the validity of the solution

• To simplify the equation

What values make the denominators x and 2x equal to zero?

• x = 2

• x = 0

• x = 1

• x = -1

What is the least common denominator (LCD) of x and 2x?

• 4x

• 3x

• 2x

• x

What is the purpose of multiplying the equation by the LCD?

• To check the solution

• To find the restrictions

• To simplify the numerators

• To eliminate the denominators

After multiplying by the LCD, what should be done next?

• Check the solution

• Simplify each term

• Find the restrictions

• Find the LCD again

What is the simplified form of 2x times 5/x?

• 10x

• 5

• 2

• 10

What is the result of simplifying 2x times 7/2x?

• 14x

• 14

• 7

• 7x

What is the next step after simplifying the equation?

• Check the solution

• Find the restrictions

• Multiply by the LCD again

• Solve for x

How do you isolate x in the equation 3 = 12x?

• Multiply by 12

• Subtract 12 from both sides

• Divide by 12

• Add 12 to both sides