Linear Inequalities
Math ⇒ Algebra
Linear Inequalities starts at 7 and continues till grade 12.
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See sample questions for grade 12
A factory produces at least 500 units per day. If x represents the number of units produced, write an inequality to represent this situation.
Describe the difference between the solution sets of the inequalities x > 2 and x ≥ 2.
Explain the difference between a strict inequality and a non-strict inequality.
Explain the effect of multiplying both sides of an inequality by a negative number.
Explain why the solution to the inequality 0 < x < 5 is called a bounded interval.
A company requires that the number of hours worked per week, h, must satisfy 20 ≤ h < 40. Which of the following values of h is NOT allowed?
(1) 20
(2) 25
(3) 40
(4) 39
A factory produces at least 500 units per day. If x represents the number of units produced, write an inequality to represent this situation.
A student claims that the solution to the inequality 2x < 2x + 1 is all real numbers. Is the student correct?
A company requires that the number of hours worked per week, h, must satisfy 20 ≤ h < 40. Which of the following values of h is NOT allowed?
(1) 20
(2) 25
(3) 40
(4) 39
Which of the following is NOT a solution to the inequality 5 - 2x ≥ 1?
(1) x = 1
(2) x = 2
(3) x = 0
(4) x = -1
Which of the following is the correct graph for the solution of x ≤ -1?
(1) A ray to the left from -1, including -1
(2) A ray to the right from -1, including -1
(3) A ray to the left from -1, not including -1
(4) A ray to the right from -1, not including -1
Which of the following is the correct interval notation for the solution to x > -2?
(1) (-2, ∞)
(2) [-2, ∞)
(3) (-∞, -2)
(4) (-∞, -2]
Fill in the blank: If 5x - 2 ≤ 3x + 6, then x ≤ _______.
Fill in the blank: The solution set of the inequality 2x - 1 ≥ 3 is x ≥ _______.
Fill in the blank: The solution set of the inequality x + 3 < 7 is x < _______.
If 2x - 3 > 7, then x > _______.
A student claims that the solution to the inequality 2x < 2x + 1 is all real numbers. Is the student correct?
True or False: The solution to the inequality -2x > 6 is x < -3.
True or False: The solution to the inequality 3x + 2 > 3x + 5 is x > 1.
True or False: The solution to the inequality 6x - 4 < 2x + 8 is x < 3.
