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 10
Describe the difference between solving a rational equation and a rational inequality.
Describe what is meant by the 'sign chart' method for solving rational inequalities.
Explain the steps to solve a rational inequality such as \( \frac{3x+1}{x-2} < 0 \).
Explain why the solution to \( \frac{1}{x} > 2 \) is x > 0 and x < \frac{1}{2}.
Explain why you must exclude values that make the denominator zero when solving rational inequalities.
Solve \( \frac{2x+1}{x-3} < 0 \).
Solve \( \frac{2x+3}{x-4} > 1 \).
Solve \( \frac{3x+2}{x-1} \leq 0 \).
If \( \frac{x-3}{x+2} < 0 \), which of the following is true? (1) x < -2 (2) -2 < x < 3 (3) x > 3 (4) x < 3
Which of the following intervals is the solution to \( \frac{x-2}{x+3} < 0 \)? (1) x < -3 (2) -3 < x < 2 (3) x > 2 (4) x < 2
Which of the following is a necessary step when solving rational inequalities? (1) Multiply both sides by the denominator (2) Find the zeros of the numerator and denominator (3) Ignore the denominator (4) Substitute x = 0
Which of the following is a solution to \( \frac{x-2}{x+2} \geq 0 \)? (1) x = -3 (2) x = 0 (3) x = 2 (4) x = -2
A rational inequality is an inequality that contains a _______ expression.
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 expression \( \frac{x-4}{x+2} \) is undefined when x = _______.
Fill in the blank: The solution to \( \frac{3x-6}{x+5} < 0 \) is _______ < x < _______.
True or False: The solution to \( \frac{1}{x} > 0 \) is all real numbers except x = 0.
True or False: The solution to \( \frac{1}{x+1} < 0 \) is x < -1.
True or False: The solution to \( \frac{1}{x-2} \leq 0 \) is x < 2.
True or False: The solution to \( \frac{2x-1}{x+3} > 0 \) is x < -3 or x > 0.5.
