Understanding Rational Equations

What is the least common denominator used to solve the equation X/3 + 2X/5 = 22?

• 3

• 15

• 10

• 5

In the equation 3x/(x-5) - 5 = 5/(x-5), what does x equal after solving?

• 10

• 5

• 15

• 0

What is the purpose of placing a '1' under the number 5 in the equation 3x/(x-5) - 5 = 5/(x-5)?

• To eliminate the variable x

• To add value to the equation

• To maintain the format of a fraction

• To simplify the equation

What does the distributive property help with in solving rational equations?

• Ensuring correct multiplication across terms

• Isolating the variable x

• Finding the least common denominator

• Simplifying the equation to a single fraction

Why is there no solution for the equation 3x/(x-3) = 2 + 9/(x-3)?

• x equals 3, which makes the denominator zero

• All values of x are solutions

• x equals 0, which is not in the domain

• The equation simplifies to 0 = 0

Why is it important to check the domain of the solution in rational equations?

• To simplify the equation further

• To verify the equation has no typos

• To confirm the equation is balanced

• To ensure the denominator does not become zero

What are the correct answers for the first two checkpoint problems?

• -1 and 4

• 4 and -4

• 0 and 1

• 1 and -1

In the equation 2x/(x-2) = 1/(3x-4) + 2, what is the value of x after solving?

• 14/11

• 11/14

• 3/2

• 2/3

What is the result of applying the least common multiple in the advanced problem-solving section?

• Conversion of all terms to whole numbers

• Introduction of new variables

• Simplification of complex fractions

• Elimination of the variable x

What technique is used to solve the equation involving 2x/(x-2) and 1/(3x-4) + 2?

• Subtracting the lowest common multiple

• Dividing by the greatest common divisor

• Multiplying by the least common multiple

• Adding the highest common factor