Hello girls, boys, aunts, uncles, hello everyone! I wish all of us in life happiness and luck. Today we are starting to study the topics of the new chapter of Inequality. The concept itself is already known to us both from life and from mathematics. In life, inequalities are more than equalities, which means we must know the methods of solving at least mathematical inequalities. By learning how to solve inequalities in mathematics, perhaps you will learn how to solve inequalities in life. And now remember the once studied.
CORRECT or WRONG? Is the comparison of numbers 3.675\u003e 3.6748 correct? 3.6748 "\u003e 3.6748"\u003e 3.6748 "title \u003d" (! LANG: CORRECT or INCORRECT? Is the comparison of the numbers 3.675\u003e 3.6748 correct?"> title="CORRECT or WRONG? Is the comparison of numbers 3.675\u003e 3.6748 correct?"> !}
CORRECT or WRONG? Is the comparison of numbers 5/7\u003e 5/8 performed correctly? 5/8 "\u003e 5/8"\u003e 5/8 "title \u003d" (! LANG: CORRECT or INCORRECT? Is the comparison of numbers 5/7\u003e 5/8 correct?"> title="CORRECT or WRONG? Is the comparison of numbers 5/7\u003e 5/8 performed correctly?"> !}
CORRECT or WRONG? Is the comparison of numbers 5/17\u003e 4/17 performed correctly? 4/17 "\u003e 4/17"\u003e 4/17 "title \u003d" (! LANG: CORRECT or INCORRECT? Is the comparison of numbers 5/17\u003e 4/17 correct?"> title="CORRECT or WRONG? Is the comparison of numbers 5/17\u003e 4/17 performed correctly?"> !}
CORRECT or WRONG? Is the comparison 3/4\u003e 2/3 correct? 2/3 "\u003e 2/3"\u003e 2/3 "title \u003d" (! LANG: CORRECT or INCORRECT? Is the comparison 3/4\u003e 2/3 correct?"> title="CORRECT or WRONG? Is the comparison 3/4\u003e 2/3 correct?"> !}
So, we found out that when comparing two figures, the figure that turned out to be larger in size when superimposed will be large. What mathematical action can compare numbers? If the difference is positive, then the first number is greater; If the difference is negative, then the first number is less.
The first number a will be greater than the second number b if? a - b 0 a-b \u003d 0 a - b 0 0 "\u003e 0"\u003e 0 "title \u003d" (! LANG: The first number a will be greater than the second number b if? A - b 0 a-b \u003d 0 a - b 0"> title="The first number a will be greater than the second number b if? a - b 0 a-b \u003d 0 a - b 0"> !}
We carry out the task of control. 730 Is the inequality a) 4x (x + 0.25)\u003e (2x + 3) (2x - 3) true for any x? This inequality is true only if x\u003e -9 (2x + 3) (2x - 3)? Is this inequality true only if x\u003e -9 "\u003e (2x + 3) (2x - 3)? Is this inequality true only if x\u003e -9"\u003e (2x + 3) (2x - 3)? This inequality is true only under the condition that x\u003e -9 "title \u003d" (! LANG: Perform the task of control. 730 Does inequality a hold true for any x) 4x (x + 0.25)\u003e (2x + 3) (2x - 3)? This inequality is true only if x\u003e -9"> title="We carry out the task of control. 730 Is the inequality a) 4x (x + 0.25)\u003e (2x + 3) (2x - 3) true for any x? This inequality is true only if x\u003e -9"> !}
We carry out the task of control. 730 Is the inequality true for any x?) (5x -1) (5x + 1) 
3x (x + 16)? The final inequality is 6x 2 + 64\u003e 0 It is true for any x, since x 2 0 for any x, and 64\u003e 0. "title \u003d" (! LANG: We carry out the task of control. 730 Is the inequality c true for any x) (3x + 8) 2\u003e 3x (x + 16)? The final inequality 6x 2 + 64\u003e 0 is true for any x, since x 2 0 for any x, and 64\u003e 0." class="link_thumb"> 21 !} We carry out the task of control. 730 Is the inequality c) (3x + 8) 2\u003e 3x (x + 16) true for any x? The final inequality 6x\u003e 0 is true for any x, since x 2 0 for any x, and 64\u003e 0. 3x (x + 16)? The final inequality 6x 2 + 64\u003e 0 is true for any x, since x 2 0 for any x, and 64\u003e 0. "\u003e 3x (x + 16)? The final inequality 6x 2 + 64\u003e 0 is true for any x, so like x 2 0 for any x, and 64\u003e 0. "\u003e 3x (x + 16)? The final inequality is 6x 2 + 64\u003e 0 It is true for any x, since x 2 0 for any x, and 64\u003e 0. "title \u003d" (! LANG: We carry out the task of control. 730 Is the inequality c true for any x) (3x + 8) 2\u003e 3x (x + 16)? The final inequality 6x 2 + 64\u003e 0 is true for any x, since x 2 0 for any x, and 64\u003e 0."> title="We carry out the task of control. 730 Is the inequality c) (3x + 8) 2\u003e 3x (x + 16) true for any x? The final inequality 6x 2 + 64\u003e 0 is true for any x, since x 2 0 for any x, and 64\u003e 0."> !}
The expressions 3a (a + 6) and (3a + 6) (a + 4) are given. Substitute numerical values \u200b\u200binstead of a and compare it with the final inequality a \u003d -5 a \u003d 0 a \u003d 5 a \u003d 
To summarize the first lesson in the study of numerical inequalities. a 2 0 We know that the square of any number is a non-negative number. Therefore, the inequality is true, which was required to be proved! a (a + b) - ab 0 After opening the brackets and simplifying, we obtain To prove the inequality a (a + b) ab, we Find the difference between the left and right expressions
Finished by: I.G. Gabarveva, teacher of mathematics, category I, secondary school № 46, Khabarovsk
Algebra lesson in 8th grade. Theme: "Social Inequality.
Numerical inequalities. "
The purpose of the lesson: To develop mathematical thinking and the ability to reproduce thoughts through oral and written speech.
Tasks:
Didactic: 1) derive a definition of numerical inequality; 2) to formulate the rules of numerical inequalities.
Psychological: Develop creativity.
Educational: Strengthen self-management ability.
Lesson plan:
I. Indicative and motivational stage .
In the most general form, inequality means that people live in conditions in which they have unequal access to the limited resources of material and spiritual consumption. Fulfilling qualitatively unequal working conditions, satisfying social needs to varying degrees, people sometimes find themselves engaged in economically heterogeneous work, because such types of labor have different estimates of their social utility. Social inequality is perceived and experienced by many people (primarily unemployed) as a manifestation of injustice. Social inequality, property stratification of society, as a rule, lead to an increase in social tension.
Social inequality is a form of social differentiation in which individuals are at different levels of the vertical hierarchy and have unequal life chances and opportunities to satisfy needs.Those. inequality is when there is no equality.
Then move on to math
Teacher Activities (Questions)
The solution of the educational task (task 1-5).
II. Operational stage.III. Reflective assessment stage.
Summarizing the result of the lesson (task 6).
Self-esteem.
Homework (task 8).
Examples of rules to which all numbers are subordinate
count Numerical inequalities and rules for all real numbers
Examples of numerical inequalities
3. 2.
4. 5.
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