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 11
Describe the difference between solving a rational equation and a rational inequality.
Explain the role of test points in solving rational inequalities.
Explain the steps to solve a rational inequality of the form \( \frac{P(x)}{Q(x)} > 0 \).
Explain why it is important to check for extraneous solutions when solving rational inequalities.
Explain why the sign of the denominator is important when solving rational inequalities.
Solve for x: \( \frac{2x+3}{x-1} \leq 0 \)
Solve for x: \( \frac{3x+1}{x-2} < 2 \).
A student claims that multiplying both sides of a rational inequality by the denominator is always valid. Is this correct? Yes or No.
Which of the following intervals is the solution to \( \frac{x+4}{x-1} > 0 \)? (1) x < -4 or x > 1, (2) x > -4 and x < 1, (3) x > -4 or x < 1, (4) x < -4 and x > 1
Which of the following intervals is the solution to \( \frac{x-5}{x+2} < 0 \)? (1) x < -2, (2) -2 < x < 5, (3) x > 5, (4) x < 5
Which of the following is a correct step in solving \( \frac{x-3}{x+2} \leq 0 \)? (1) Multiply both sides by (x+2) without considering its sign, (2) Find critical points at x = 3 and x = -2, (3) Ignore the denominator, (4) Substitute x = 0 only
Which of the following is a solution to \( \frac{2x-3}{x+4} \geq 0 \)? (1) x = -5, (2) x = 2, (3) x = -4, (4) x = 1
Fill in the blank: The inequality \( \frac{x+1}{x-4} < 0 \) is satisfied for _____ < x < _____.
Fill in the blank: The inequality \( \frac{x-4}{x+2} \geq 0 \) is satisfied for x \geq _____ or x < _____ (excluding any values that make the denominator zero).
Fill in the blank: The solution to \( \frac{2x+5}{x-3} < 0 \) is _____ < x < _____.
Fill in the blank: The solution to \( \frac{3x+1}{x-2} \geq 0 \) is x \geq _____ or x < _____.
A rational inequality has a solution set that is the union of intervals. True or False?
A rational inequality is undefined at values that make the denominator zero. True or False?
A student claims that multiplying both sides of a rational inequality by the denominator is always valid. Is this correct? Yes or No.
True or False: The solution to \( \frac{1}{x} < 0 \) is all negative real numbers except zero.
