Algebraic Concepts and Techniques

The video tutorial covers examples of rational expressions and equations for the SAT math section. It begins with simplifying rational expressions by factoring and canceling common factors. The tutorial then moves on to solving for X in rational equations by isolating the variable using reciprocals. Advanced techniques for solving equations with X are demonstrated, including factoring and rearranging terms. Finally, the video explains how to compare coefficients in equations to find solutions, emphasizing the importance of standard form and algebraic manipulation.

What is the first step in simplifying a rational expression?

• Subtract the numerator from the denominator

• Factor the numerator and denominator

• Add the numerator and denominator

• Multiply the numerator and denominator

Which pair of numbers multiplies to -12 and adds up to -4?

• 1 and -12

• 4 and -3

• 2 and -6

• 3 and -4

What is the greatest common factor of 3, -9, and -30?

• 3

• 30

• 1

• 9

How do you isolate X in an equation with a fraction?

• Add the reciprocal to both sides

• Subtract the reciprocal from both sides

• Divide by the reciprocal on both sides

• Multiply by the reciprocal on both sides

What is the reciprocal of 3a²B over 4Cⁿ+5?

• 1 over 3a²B

• 3a²B over 4Cⁿ+5

• 4Cⁿ+5 over 3a²B

• 1 over 4Cⁿ+5

In the equation a = x + 1 over x - B, what is the first step to solve for X?

• Add B to both sides

• Multiply both sides by x - B

• Subtract 1 from both sides

• Divide both sides by x + 1

What is the result of factoring out X from X - aX?

• X - a

• X + a

• X(a - 1)

• X(1 - a)

If aX + 4 times BX - 2 equals 21x² + CX - 8, what is the first step to find C?

• Add 8 to both sides

• Combine like terms

• Subtract 21x² from both sides

• Multiply both sides by 2

What are the possible values of C if a + B = 10 and aB = 21?

• 22 and -2

• 10 and 21

• 21 and 10

• 22 and 10

How do you determine the number of X's on the left side of the equation?

• By factoring out X

• By adding all coefficients

• By dividing by the coefficient of X

• By multiplying all terms