Inequalities

Học bằng cách chơi

Trả lời những câu hỏi này để kiếm năng lượng, rồi câu cá và khám phá. Không cần tài khoản.

Dành cho nhà giáo dục: slide bài học, ghi chú ôn tập sẵn dùng cho Inequalities (Mathematics, Algebra) — dùng trong bài giảng của bạn, hoặc chạy chủ đề như một hoạt động lớp học tương tác để người học chơi như một trò chơi trực tiếp.

Ghi chú bài học Slide Câu hỏi luyện tập

Ghi chú bài học

Inequality symbols

< less than, > greater than, \leq less than or equal to, \geq greater than or equal to.
-2 < x \leq 3 means x is greater than -2 and at most 3. Integers satisfying it: -1, 0, 1, 2, 3.

Solving linear inequalities

Solve like an equation, doing the same to both sides. The answer is a range: 3x + 2 > 11 gives x > 3.
Reverse the inequality sign if you multiply or divide by a negative number: -2x < 8 gives x > -4.

Number lines and set notation

A filled circle shows the end value is included (\leq, \geq); an open circle shows it is excluded (<, >).
Write a double inequality such as -1 \leq x < 4 as one range on a number line.

Quadratic inequalities

Solve x² - x - 6 < 0: factorise (x - 3)(x + 2) < 0. Roots -2 and 3. The parabola is below the axis between the roots, so -2 < x < 3.
For x² > 9: x < -3 or x > 3.

Where the quadratic is negative

Graphical inequalities

Draw a solid boundary for ≤ or ≥, and a dashed boundary for < or >. Test a point not on the boundary to choose the required side; the origin works only if it is off the boundary.
Regions defined by several inequalities: shade out the unwanted regions and leave the required region unshaded, or as the question states.

Slide

Step through every slide for this topic — plus flashcards and revision notes — with a free account.

ĐĂNG KÝ — MIỄN PHÍ ĐĂNG NHẬP

Câu hỏi luyện tập

Xem trước miễn phí — 8 trên 34 câu hỏi. Đăng ký để xem tất cả.

1.Which symbol means "less than or equal to"?
Easy
- A<
- B\leq
- C>
- D\geq
2.Solve x + 4 < 10.
Easy
- Ax < 6
- Bx > 6
- Cx < 14
- Dx > 14
3.Solve 2x \geq 8.
Easy
- Ax \geq 4
- Bx \leq 4
- Cx \geq 16
- Dx \geq 6
4.Which integers satisfy -2 < x \leq 1?
Easy
- A-1, 0, 1
- B-2, -1, 0, 1
- C-1, 0
- D-2, -1, 0
5.Solve 3x - 5 \leq 10.
Easy
- Ax \leq 5
- Bx \geq 5
- Cx \leq 15
- Dx \leq 1.67
6.Solve -2x < 8.
Easy
- Ax < -4
- Bx > -4
- Cx < 4
- Dx > 4
7.Solve 5 - x > 2.
Easy
- Ax > 3
- Bx < 3
- Cx > -3
- Dx < -3
8.What does an open circle on a number line mean?
Easy
- Athe value is included
- Bthe value is not included
- Cthe value is negative
- Dthere is no solution

Thêm câu hỏi

9.What does a filled circle on a number line mean?
Easy
- Athe value is included
- Bthe value is excluded
- Cmultiplied by 2
- Dno solution
10.Solve 2(x - 3) < 10.
Medium
- Ax < 8
- Bx < 5
- Cx > 8
- Dx < 13
11.Solve 4x + 1 \geq 7x - 8.
Medium
- Ax \leq 3
- Bx \geq 3
- Cx \leq -3
- Dx \geq 9
12.Solve -3 \leq 2x + 1 < 7.
Medium
- A-2 \leq x < 3
- B-4 \leq x < 6
- C-2 \leq x < 4
- D-1 \leq x < 3
13.How many integers satisfy -3 \leq 2x + 1 < 7?
Medium
- A4
- B5
- C6
- D3
14.The largest integer satisfying 3x - 2 < 13 is:
Medium
- A4
- B5
- C6
- D3
15.Solve x² < 16.
Medium
- Ax < 4
- B-4 < x < 4
- Cx > 4 or x < -4
- Dx < -4
16.Solve x² - x - 6 < 0.
Medium
- A-2 < x < 3
- Bx < -2 or x > 3
- C-3 < x < 2
- Dx < 3
17.Solve x² > 9.
Medium
- Ax > 3
- B-3 < x < 3
- Cx < -3 or x > 3
- Dx > -3
18.Solve x² - 5x + 4 \geq 0.
Medium
- A1 \leq x \leq 4
- Bx \leq 1 or x \geq 4
- Cx \geq 4
- Dx \leq 4
19.What is the largest integer n for which n² < 50?
Medium
- A7
- B8
- C6
- D25
20.On a graph, the boundary for y > 2x is:
Easy
- Asolid
- Bdashed
- Cdotted vertical
- Dabsent
21.On a graph, the boundary for y \leq 3 is:
Easy
- Asolid
- Bdashed
- Cabsent
- Dcurved
22.Which listed point can be used to test a side of the boundary y = x + 1 for the inequality y < x + 1?
Medium
- A(0, 0)
- B(1, 2), on the boundary
- CNo test point is needed
- D(2, 3), on the boundary
23.Which inequality describes the region below the line y = 4, including the line?
Medium
- Ay < 4
- By \leq 4
- Cy > 4
- Dy \geq 4
24.Which point satisfies y > x and y < 5?
Medium
- A(1, 3)
- B(3, 1)
- C(2, 5)
- D(6, 4)
25.Which inequality means "x is at least 5"?
Easy
- Ax > 5
- Bx \geq 5
- Cx < 5
- Dx \leq 5
26.Which inequality means "x is less than 10"?
Easy
- Ax \leq 10
- Bx < 10
- Cx > 10
- Dx \geq 10
27.When multiplying or dividing an inequality by a negative number, the sign flips.
Easy
True or false?
28.x \leq 3 is shown with an open circle.
Easy
True or false?
29.x² > 4 means x > 2 only.
Easy
True or false?
30.The solution of x² < 4 is -2 < x < 2.
Easy
True or false?
31.-3x > 6 gives x > -2.
Medium
True or false?
32.Which of these integers satisfy 2 < x \leq 6?
Medium
- A2
- B3
- C4
- D6
- E7
33.Which values satisfy x \geq 3?
Medium
- A3
- B2.5
- C4
- D10
- E2.99
34.Solve x² - x - 6 < 0 and write the solution as an inequality.
Medium

Unlock all 34 questions & more

Tạo tài khoản miễn phí để xem mọi câu hỏi, slide, thẻ ghi nhớ và ghi chú ôn tập cho chủ đề này.

ĐĂNG KÝ — MIỄN PHÍ ĐĂNG NHẬP

Đề thi cũ

Luyện đề thi cũ cho chủ đề này sắp ra mắt.

Sắp ra mắt