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 12
Describe the difference between solving a rational equation and a rational inequality.
Describe the process of solving a rational inequality.
Explain the steps to solve \( \frac{3x+1}{x-2} < 2 \).
Explain why multiplying both sides of a rational inequality by the denominator can be problematic.
Explain why the sign of the denominator is important when solving rational inequalities.
Explain why values that make the denominator zero must be excluded from the solution set of a rational inequality.
If \( \frac{x^2-9}{x+1} \geq 0 \), what is the solution set?
Solve \( \frac{2x+1}{x-4} \leq 0 \) and write the solution set.
Which of the following intervals is NOT part of the solution to \( \frac{2x+3}{x-4} > 0 \)? (1) (-\infty, -1.5), (2) (4, \infty), (3) (-1.5, 4), (4) (4, 10)
Which of the following is a correct method to solve \( \frac{x-1}{x+2} > 0 \)? (1) Find where numerator and denominator are zero, (2) Multiply both sides by x+2, (3) Substitute x = 0, (4) Ignore the denominator
Which of the following is a correct step in solving \( \frac{x-2}{x+5} \geq 1 \)? (1) Multiply both sides by (x+5) without considering its sign, (2) Bring all terms to one side and combine into a single rational expression, (3) Substitute x = 0, (4) Ignore the denominator
Which of the following is a necessary step when solving \( \frac{x-3}{x+2} \leq 0 \)? (1) Ignore the denominator, (2) Find where numerator and denominator are zero, (3) Only solve for x in the numerator, (4) Multiply both sides by the denominator without checking its sign
Fill in the blank: The inequality \( \frac{3x-2}{x+4} > 0 \) is satisfied for x > _____ or x < _____.
Fill in the blank: The inequality \( \frac{5}{x-1} > 0 \) is satisfied for x > _____
Fill in the blank: The inequality \( \frac{x+1}{x-4} \geq 0 \) is satisfied for x \geq _____ or x < _____.
Fill in the blank: The inequality \( \frac{x+3}{x-2} > 0 \) is satisfied for x > _____ or x < _____.
True or False: The solution to \( \frac{1}{x} \geq 2 \) is x \leq 0.5.
True or False: The solution to \( \frac{1}{x} < 0 \) is all negative real numbers except zero.
True or False: The solution to \( \frac{1}{x-2} > 0 \) is x > 2.
True or False: The solution to \( \frac{x^2-4}{x+1} \leq 0 \) is x \in (-1, 2].
