Exploring Rational Equations and Proportions

The video tutorial introduces solving rational equations, focusing on proportions. It begins with a review of solving proportions in geometry, using similar triangles as examples. The tutorial then progresses to solving proportions in Algebra 1, emphasizing cross multiplication and solution verification. It advances to Algebra 2, where more complex proportions involving quadratics are solved using factoring and the quadratic formula. The video concludes with a discussion on verifying solutions and identifying extraneous solutions.

What is a proportion in the context of rational equations?

• An equation with no variables

• A fraction with a variable in the numerator

• Two fractions with an equal sign between them

• An equation with an equal sign

In the proportion 6 is to X as 4 is to 6, what is the value of X?

• 8

• 9

• 6

• 12

What is the first step in solving the proportion 3 over X equals 9 over 3?

• Cross multiply

• Add 3 to both sides

• Subtract 3 from both sides

• Divide both sides by 3

In the equation 3 times (2X + 4) equals X squared minus 3X plus 2X minus 6, what is the first step to simplify the right side?

• Subtract 6 from both sides

• Factor the equation

• Add 6 to both sides

• Combine like terms

What method can be used to solve the quadratic equation X squared minus 7X minus 18 equals 0?

• Cross multiplication

• Addition and subtraction

• Quadratic formula

• Graphing

What is an extraneous solution?

• A solution that is a fraction

• A solution that is a whole number

• A solution that satisfies the original equation

• A solution that does not satisfy the original equation

In the equation 4X plus 20 equals X squared minus 1, what is the next step after combining like terms?

• Set the equation to zero

• Divide both sides by X

• Add 1 to both sides

• Subtract 20 from both sides

What are the solutions to the equation X squared minus 4X minus 21 equals 0?

• 7 and -3

• 3 and -7

• 7 and 3

• -7 and -3

How do you verify if a solution works in a proportion?

• By adding the solution to both sides

• By substituting the solution back into the original equation

• By multiplying the solution by both sides

• By dividing the solution by both sides

What should you do if you get a zero in the denominator while checking a solution?

• Mark it as an extraneous solution

• Divide by zero

• Consider it as a valid solution

• Ignore it