"End of Chapter Review Improvement Course" Equality and Inequality PPT

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"End of Chapter Review Improvement Course" Equality and Inequality PPT

Part One Content: Comprehensive Improvement

Application of Inequality Properties

(1) Which of the following propositions is correct ()

①If a>1, then 1a<1; ②If a+c>b, then 1a<1b; ③For any real number a, a2≥a; ④If ac2>bc2, then a>b.

A． 1 B. 2

C. 3 D. 4

(2) Given that 2

regular method

When judging the true or false of a proposition about an inequality, first connect the proposition to be judged with the properties of the inequality, find properties similar to the proposition, and use the properties to determine the true or false of the proposition. Pay attention to the application of the special value method in solving objective problems related to inequalities.

Track training

It is known that a, b, c∈R, then the correct one of the following propositions is ()

A． If a>b, then ac2>bc2 B. If ac>bc, then a>b

C. If a3>b3 and ab<0, then 1a>1b D. If a2>b2 and ab>0, then 1a<1b

Solutions to groups of inequalities

(1) Solve the inequality group:

5x-1<3 (x+1), 2x-13-1≤5x+12;

(2) It is known that the inequality group x+a≤0 about x, and there are only three integer solutions to ①3+2x>5②, find the value range of a.

regular method

(1) The key to solving a set of linear inequalities of one variable is to master the rules for determining the common parts of the solution sets of each inequality; if they are the same, get the larger, if they are the same, get the smaller, find the big or small in the middle, and find the big or small nowhere.

(2) Determine the value or value range of the letter parameter from the solution set or special solution of the known inequality (set). The commonly used solution method is to first use the method of solving the inequality (set) to find the inequality (set) containing the letter parameter ), and then substitute it into the given conditions, the value or value range of the letter parameter can be obtained.

Solution to Absolute Value Inequality

Solve the following inequalities:

(1)|2x+1|-2|x-1|>0;

(2)|x＋3|－|2x－1|＜x2＋1.

regular method

Solution: |x-a|＋|x-b|≥c, |x-a|+|x-b|≤c type

General steps for inequalities

(1) Let the linear expression in each absolute value symbol be zero and find the corresponding root.

(2) Sort these roots from small to large and divide the real number set into several intervals.

(3) Several inequalities are formed by removing the absolute value sign from the partitioned intervals, solving these inequalities, and finding their solution sets.

(4) The union of the solution sets of these inequalities is the solution set of the original inequality.

End-of-Chapter Review Improvement Lesson PPT, Part 2 Content: Literacy Improvement

1. It is known that the set M={x|-4≤x≤7}, N={x|x2-x-12>0}, then M∩N=()

A． {x|-4≤x<-3 or 4

B． {x|-4

C. {x|x≤-3 or x>4}

D. {x|x<-3 or x≥4}

2. It is known that a>b>0, then the following inequality must be true ()

A． a+1b>b+1aB． a+1a≥b+1b

C. ba>b+1a+1 D. b-1b>a-1a

3． The solution set of the inequality |x＋1|-|x-2|≥1 is ________.

4. Solve the inequality:

(1)x2－4x－5≤0;

(2)-x2+6x-10>0;

(3)-2x2+3x-2<0.

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For more information about the PPT courseware "End-of-Chapter Review and Improvement Lesson Equations and Inequalities", please click the End-of-Chapter Review and Improvement Lesson ppt Equations and Inequalities ppt tag.

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Update Time: 2024-09-29

This template belongs to Mathematics courseware People's Education High School Mathematics Edition B Compulsory Course 1 industry PPT template

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