For the equation x + 3 x² − 4 + 1 x = 10, what value(s) of x must immediately be excluded as possible solutions to the equation?

A. -3
Incorrect. While -3 makes the numerator of the left expression 0, it could still be a solution to the equation. You only exclude values that make the denominator 0.

B. 2 and 0
Incorrect. While both of these values do make the denominator 0, -2 also makes the denominator 0.

C. 4 and 0
Incorrect. 4 does not make the denominator 0.

D. -2, 2, and 0
Correct! -2 and 2 both make the quantity equal to 0, and 0 makes the equal 0. They must be excluded.

What is the solution to the equation -x − 8 x + 2 = 2 x + 2?

A. x = -10
Correct! The algebraic solutions to the equations are -2 and 10 but the solution -2 is excluded since it would create a zero in the denominator.

B. x = -8
Incorrect. This makes the numerator equal to 0, but it is not a solution to the equation.

C. x = -2 or x = -10
Incorrect. -2 must be excluded from the solution set because it makes the denominator 0.

D. x = -4 or x = -5
Incorrect. You may have factored your quadratic equation improperly. Check that step and try again.

Solve the equation 5 x + 3 x − 2 = 6 x(x − 2).

A. x = 0 or x = 2
Incorrect. Neither of these values for x could be solutions since they both make the denominators 0.

B. x = 2
Incorrect. While this is the solution you get when you solve the equation algebraically, it must be excluded because it makes the denominator 0.

C. x = 1
Incorrect. You may have incorrectly distributed a factor during your solution. Try again.

D. No solution
Correct! The algebraic solution to the equation is 2 but 2 makes the denominator 0, therefore, there are no solutions to this equation.

What is the solution of the equation 6x x + 4 + 4 = 2x + 2 x − 2?

A. x = -1
Incorrect. While -1 makes the numerator 0, it is not a solution to the equation.

B. x = 0 or x = -1
Incorrect. Neither of these values are solutions to the equation.

C. x = -3 2 or x = 2
Correct! The solutions to the equation are 2 and -3 halves which are both possible since -4 and 1 would create a zero in the denominator.

D. x ≠ -4 or x ≠ 1
Incorrect. These are the values that would be excluded from the solution set, but they are not the solutions to the equation.