Linear Inequalities
Math ⇒ Algebra
Linear Inequalities starts at 7 and continues till grade 12.
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See sample questions for grade 11
Context: A company requires that the number of hours worked per week, h, must be at least 35 but no more than 45. Write the inequality that represents this situation.
Explain why multiplying both sides of an inequality by a negative number reverses the inequality sign.
If -2x + 7 ≤ 1, what is the greatest integer value of x?
If a linear inequality has no solution, what does this mean?
Solve for x: 2(x - 1) ≤ 8.
Solve for x: -5x + 10 > 0.
Solve for x: 5x + 3 > 2x - 6.
Context: A company requires that the number of hours worked per week, h, must be at least 35 but no more than 45. Write the inequality that represents this situation.
If a solution to an inequality is x < 7, which of the following statements is true?
(1) x can be equal to 7
(2) x must be less than 7
(3) x must be greater than 7
(4) x can be any real number
If the solution to an inequality is x > 0, which of the following numbers is NOT a solution?
(1) 1
(2) 0.5
(3) 0
(4) 2
Which of the following intervals represents the solution to x < -1 or x > 3?
(1) (-∞, -1) ∪ (3, ∞)
(2) (-1, 3)
(3) [-1, 3]
(4) (-∞, 3)
Which of the following is a correct step when solving the inequality 3x - 4 < 8?
(1) Add 4 to both sides
(2) Subtract 4 from both sides
(3) Multiply both sides by 3
(4) Divide both sides by 3
Fill in the blank: If x > 2, then 3x > _______.
Fill in the blank: The solution to the inequality -3x > 12 is x < _______.
Fill in the blank: The solution to the inequality 4 - x ≥ 1 is x ≤ _______.
Fill in the blank: The solution to the inequality 5x < 20 is x < _______.
If the inequality sign is reversed when both sides are multiplied by a negative number, is this always true?
True or False: The solution set of 2x - 3 ≥ 7 is x ≥ 5.
True or False: The solution set of 2x + 5 < 1 is x < -2.
True or False: The solution set of x - 4 > 2 is x > 6.
