Inequalities with Rational Expressions
Math ⇒ Algebra
Inequalities with Rational Expressions starts at 9 and continues till grade 12.
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See sample questions for grade 9
Describe the difference between solving a rational equation and a rational inequality.
Describe the process of finding the solution set for \( \frac{ax+b}{cx+d} < 0 \).
Explain the steps to solve a rational inequality such as \( \frac{2x-1}{x+5} \geq 0 \).
Explain why it is important to exclude values that make the denominator zero when solving rational inequalities.
Explain why the solution to \( \frac{1}{x} \geq 0 \) does not include x = 0.
If \( \frac{2x-1}{x+4} \leq 0 \), what is the solution set?
If \( \frac{x+2}{x-4} \geq 0 \), what is the solution set?
If \( \frac{x-4}{x+2} < 0 \), what is the solution set?
If \( \frac{2x-5}{x+3} > 0 \), which of the following is a possible value for x? (1) x = -4 (2) x = 0 (3) x = -2 (4) x = -3
Which of the following intervals is the solution to \( \frac{4x}{x-2} < 0 \)? (1) x < 0 (2) 0 < x < 2 (3) x > 2 (4) x < 2
Which of the following intervals is the solution to \( \frac{x+3}{x-2} > 0 \)? (1) x < -3 or x > 2 (2) -3 < x < 2 (3) x > -3 and x < 2 (4) x < -3 and x > 2
Which of the following intervals is the solution to \( \frac{x-2}{x+4} < 0 \)? (1) x < -4 (2) -4 < x < 2 (3) x > 2 (4) x < 2
Fill in the blank: The critical points of the inequality \( \frac{x+5}{x-2} \geq 0 \) are x = _______ and x = _______.
Fill in the blank: The inequality \( \frac{1}{x} < 0 \) is satisfied for all _______ values of x.
Fill in the blank: The inequality \( \frac{x+4}{x-3} < 0 \) is satisfied for values of x in the interval _______.
Fill in the blank: The solution to \( \frac{2x+1}{x-2} \leq 0 \) is _______.
True or False: The solution to \( \frac{1}{x} > 0 \) is all positive real numbers.
True or False: The solution to \( \frac{1}{x-5} > 0 \) is x > 5.
True or False: The solution to \( \frac{2x+1}{x-3} > 0 \) is x > 3 or x < -\frac{1}{2}.
True or False: The solution to \( \frac{3x-1}{x+2} \leq 0 \) is x \leq -2 or x \leq \frac{1}{3}.
