Presentation. "Solving inequalities, systems of inequalities." presentation of a lesson for an interactive whiteboard in algebra (grade 8) on the topic. Presentation "Solving systems of inequalities with one variable"

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Slides captions:

Systems of linear inequalities with one unknown. Author Eremeeva Elena Borisovna teacher of mathematics, MBOU secondary school No. 26, Engels

Verbal counting. 1. Name the general solution 4 -2 0 -5 2. Solve the inequalities: a) 3x > 15 b) -5x ≤ -15 3. What is the comparison sign for positive numbers?

Is the number in brackets the solution to the system of inequalities? 2 x + 3 > 0, (-1) 7 - 4 x > 0. Solution: Substitute the number -1 in the system instead of the variable x. 2 (-1) + 3 > 0, -2 + 3 > 0, 1 > 0, true 7 - 4 (-1) > 0; 7 + 4 > 0; 11 > 0. correct Answer: The number -1 is the solution of the system.

Training task No. 53 (b) 5x > 10, (3) 6x + 1 10, 15 > 10, correct 6 3

Solving systems of inequalities with one unknown.

Solve the system of inequalities. 13x - 10 6x - 4. Solution: 1) Solve the first inequality of the system 13x - 10

2) Solve the second inequality of the system 10x - 8 > 6x - 4 10x -6x > - 4 + 8 4x > 4 x > 1 3) Solve the simplest system x 1 1 (1; 3) Answer: (1; 3)

Training exercises. No. 55 (f; h) f) 5x + 3 2. Solution: 1) 5x + 3 2 5x 2 - 7 5x - 5 x

No. 55 (h) 7x 5 + 3x. Solution: 1) 7x 5 + 3x 7x - x 5 - 2 6x 3 x

Additional task No. 58 (b) Find all x, for each of which the functions y \u003d 0.4x + 1 and y \u003d - 2x + 3 simultaneously take positive values. Compose and solve the system of inequalities 0.4x + 1 > 0, 0.4x > -1, x > - 2.5 - 2x + 3 > 0 - 2x > -3; X

Homework. No. 55 (a, c, e, g) Optional task No. 58 (a).

On the topic: methodological developments, presentations and notes

Lesson summary "Solving linear inequalities with one unknown"

Lesson type: learning new material Purpose: to develop with students an algorithm for solving linear inequalities with one unknown. Tasks to develop skills for solving linear inequalities with one unknown ...

The plan is a summary of the lesson in algebra “Inequalities with one unknown. Systems of inequalities»

The plan is a summary of the lesson in algebra “Inequalities with one unknown. Systems of inequalities. Algebra 8th grade. Textbook for educational institutions. Sh.A.Alimov, Yu.M.Kolyagin, Yu.V.Sidorov and others.Purpose...

• Alekseeva Tatyana Alekseevna
• BEI HE "Gryazovets comprehensive boarding school for students with disabilities by hearing"
• Mathematic teacher

• repeat numerical intervals, their intersection,
• formulate an algorithm for solving systems of inequalities with one variable,
• learn how to correctly write a solution,
• right, nice to say,
• listen attentively.

• Repetition:
• warm-up,
• math lottery.
• Learning new material.
• Consolidation.
• Summary of the lesson.

What are the inequalities?

Strict, non-strict, simple, double.

_____________________________ What number ranges do you know? _____________________________

• number lines,
• number intervals
• half-intervals
• number rays,
• open rays.

How many ways are there to indicate number intervals? List.

• With the help of inequality
• with brackets,
• verbal name of the interval,
• image on a coordinate line

1. Mathematical

Check yourself (3;6) [ 1.5 ; 5 ]

2. Mathematical

Check yourself 0; 1; 2; 3.-6; -5; -4; -3; -2; 0.

3. Mathematical

Test yourself smallest -7 largest 7 smallest -5 largest -3

4. Mathematical

Check yourself - 2 < X < 3 - 1 < Х < 4

• For correct verbal answers,
• for finding the intersection of sets,
• for 2 math tasks
lotteries,
• for helping the group
• for the answer at the blackboard.

Evaluate yourself in the warm-up

• Solve inequalities (on a draft)
• draw the solution on the coordinate line:
• 2x - 1 > 6,
• 5 - 3x > - 13;

Check yourself

2x - 1 > 6,

5 – 3x > - 13

– 3x > - 13 – 5

– 3x > - 18

Answer: (3.5;+∞)

Answer: (-∞;6)

Task number 2 Solve the system: 2x - 1 > 6, 5 - 3x > - 13. 1. We solve both inequalities simultaneously, writing the solution in parallel as a system, and the set of solutions of both inequalities is depicted on one and the same same coordinate line. solution 2x - 1 > 6 2x > 1 + 6 2x > 7 5– 3x > - 13 - 3x > - 13 - 5 - 3x > - 18 x > 3.5 2. find the intersection X< 6 two number spans: ///////////// 3,5 6 3. We write the answer as a numerical interval Answer: x (3.5; 6) Answer: x (3.5; 6) is the solution to this system. Definition. The solution of a system of inequalities with one variable is called the value of the variable for which each of the inequalities of the system is true.

See textbook definition on page 184 in paragraph 35

"Solution of systems of inequalities

with one variable...

Working with the textbook

• We solved the first and second inequalities, writing the solution in parallel as a system.
• Depicted the set of solutions to each inequality on one coordinate line.
• Found the intersection of two numerical intervals.
• Write down your answer as a number.

• Solve the first and second inequalities, writing their solutions in parallel as a system,
• depict the set of solutions of each inequality on the same coordinate line,
• find the intersection of two solutions - two numerical intervals,
• write your answer as a number.

Rate yourself on

learning new...

• Behind independent solution inequalities,
• for writing the solution of a system of inequalities,
• for the correct oral answers in the formulation of the algorithm for solving and determining,
• for the textbook.

see tutorial

page 188 on "3" No. 876

on "4" and "5" No. 877

Independent work

Examination № 876 a) X>17; b) X<5; c)0<Х<6;

№ 877

a) (6;+∞);

b) (-∞;-1);

d) decisions

No;

e) -1 < X < 3;

f)8<х< 20.

d) decisions

• For 1 mistake - "4",
• for 2-3 mistakes - "3",
• for the correct answers - "5".

Rate yourself on

independent

work

• Repeated numerical intervals;
• got acquainted with the definition of a solution to a system of two linear inequalities;
• formulated an algorithm for solving systems of linear inequalities with one variable;
• solved systems of linear inequalities based on the algorithm.
• Has the goal of the lesson been achieved?

• For repetition
• for learning new material
• for independent work.

Set yourself

grade for the lesson

Solving linear inequalities

8th grade

Test. (yes - 1, no - 0)

1 ) Is the number 12 a solution to the 2x10 inequality?

2) Is the number -6 a solution to the 4x12 inequality?

3) Is the inequality 5x-154x+14 strict?

4) Is there an integer that belongs to the interval [-2.8;-2.6]?

5) Is the inequality a² +4 o true for any value of the variable a?

6) Is it true that when both parts of the inequality are multiplied or divided by a negative number, the sign of the inequality does not change?

Solve the linear inequality:

3x - 5 ≥ 7x - 15

3x – 7x ≥ -15 + 5

-4x ≥ -10

x ≤ 2.5

Answer: (-∞; 2.5].

• Move the terms by changing the signs of the terms

2. Give like terms on the left and right sides of the inequality.

3. Divide both parts by -4, remembering to change the inequality sign.

Find an error in solving inequalities. Explain why the mistake was made. Write the correct solution in your notebook.

№ 1.

31(2x+1)-12x 50x

62x+31-12x 50x

50x-50x-31

Answer: x 0

№ 2.

3(7-4y) 3y-7

21-12y 3y-7

-12y + 3y -7-21

-9y - 28

Answer: (3 1/9 ;+ ∞)

Write the letter of the correct answer

Restore the solution to the inequality

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Slides captions:

Solving inequalities and systems of inequalities with one variable. 8th grade. x x -3 1

Repetition. 1. What inequalities correspond to intervals:

Repetition. 2. Draw a geometric model of the gaps: x -2 7 4 x -5 x -1 2 x

Repetition. 3. What inequalities correspond to geometric models: x -4 17 0 x -33 x -1 9 x

Repetition. 4. What gaps correspond to geometric models: x -4 2.5 -1.5 x 5 x 3 8 x

We solve inequalities. Solve an inequality - find the value of a variable that turns it into a true numerical inequality. Rules: 1.

We solve inequalities. Solve an inequality - find the value of a variable that turns it into a true numerical inequality. Rules: 2 . : A

We solve inequalities. Solve an inequality - find the value of a variable that turns it into a true numerical inequality. Rules: 2 . : a When dividing (multiplying) by a negative number, the inequality sign changes.

We solve inequalities. 1. -3 x Answer:

We solve inequalities. 2. -0.5 x Answer:

We solve inequalities. x -4 x 10 3 x Show the solution on the number line and write the answer as an interval:

We solve inequalities. Write your answer as an interval:

We solve inequalities. Write your answer as an inequality:

We solve the system of inequalities. Solve a system of inequalities - find the value of a variable for which each of the inequalities of the system is true. 6 3.5 Answer: Answer: x

We solve the system of inequalities. Solve a system of inequalities - find the value of a variable for which each of the inequalities of the system is true. 9 1 Answer: Answer: x

We solve the system of inequalities. Solve a system of inequalities - find the value of a variable for which each of the inequalities of the system is true. -2 Answer: no solutions 3 x

We solve the system of inequalities. -5 1 x 0.5 -3 x

Thank you for your attention! Good luck!

We solve a double inequality. : 3 5 7 Answer: x

We solve a double inequality. : -1 -5 3 Answer: x

We solve a double inequality. 5.5 0 x -1 x 3

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