Chapter 1 Linear Inequalities in One Unknown Name:_________( ) Class: ( )
Important Terms
linear inequalities | 线性不等式 | smt是什么意思additive property | 加法性质 |
transitive property | manny传递性质 | reciprocal property | 倒数性质 |
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Revision Notesexamda
1. Meanings of the inequality signs ‘’ and ‘’
(a) The inequality sign ‘’ means ‘is greater than or equal to’
e.g. means a is greater than or equal to 5.
(b) The inequality sign ‘’ means ‘is less than or equal to’
e.g. means a is less than or equal to–3.
orally2. Solutions of inequalities and their reprentation on the number line
(a) For an inequality in one unknown x, the values of x that can satisfy the inequality are called the solutions of the inequality.
(b) The solutions of the linear inequalities in one unknown can be reprented on the number line.
e.g. (i) The solutions of can be reprented as
(ii)The solutions of can be reprented as
(iii) The solutions of can be reprented as
(iv) The solutions of can be reprented as
3. Basic properties of inequalities
(a) transitive property
If and , then saks.
e.g. and fuck you什么意思, then
(b) additive property
If then .
and
(c) multiplication property
(i) If 历史英文 and , then .
e.g. and , then
(ii) If and , then .
e.g. and , then
(d) reciprocal property
If , then .
e.g. then .
(e) the above properties also hold when the inequality signs ‘’ and ‘’ are replaced by ‘’ and ‘’ respectively.
4. Linear inequalities in one unknown and their applications
(a) An inequality which has only one unknown with index 1 is called a linear inequality in one unknown.
(b) We can find the solutions of inequalities systematically by applying the basic properties of inequalities.
(c) There are many daily life problems that involve the concept of inequalities. Sometimes we can t up simple inequalities in one unknown to find the relevant solutions, but we must consider if the answers obtained suit the real situation.
Exerci A
Level 1
1. Fill in each of the following blanks with an inequality sign 「>」、「<」、「」or「」
(a) If x > 4 and 4 > y , then x ____ y. (b) If 5 < x and x < y, then y ____ 5.
(c) If us ady8 infoa > 3 and 3 b , then a ____ b. (d) If a 1 amd 1 < b, then a ____ b.
(e) If a 5 and 5 < x , then a ____ x. (f) If x < 3 then x 1 ____ 4.
(g) If y 2, then y 3 ____ 1. (h) If x 5, then 5x 2 ____ 23.
(i) If a < 9, then 4a 3 ____ 33.
2. Write down an inequality in x corresponding to each of the following diagrams.
(a) (b)刀子的英语
____________ ___________
(c) (d)
____________ ___________
3. Reprent the solutions of each of the following inequalities graphically on the number line..
(a) (b)
4. Solve the following linear inequalities in one unknown and reprent their solutions graphically on the number line.
(a) 5 2x > 0 (b) x 6 < 2
(c) 3x 1 < 2x 5 (b) 2 < 5 x
Level II
5. If x > y > 0 , fill in each of the following blanks with an inequality sign ‘>’ or ‘<’.
(a) ________ (b) _________
6. If x > y，x > 0 and y < 0, fill in each of the following blanks with an inequality sign.
(a) ______ (b) _________
7. Solve the following linear inequalities in one unknown and reprent their solutions graphically on the number line.
(a) 4x 21 < 3 (b)
(c) (d)
(e) (f)
(g) (h)
8. Find the largest integer that can satisfy the inequality .
