Question

1)3х-15=х+3 2)7-3х=х+11 3)2(х+3)=х+13 4)4(5-х)=3х-1 5)3(х-2)=х+4 6)5(х-1)=4х+3   задание № 2 Запишите с помощью неравенств 1)скорость автомашины больше 40 км/ч,но меньше 60 км/ч 2) в секции легкой атлетики в одной группе занимаются не меньше 12 учеников,но не больше 16

Answer 1

Вычислим значение х:
1) 3х-15=х+3
3х-х=3+15
2х=18
х=9
Ответ: х=9 (проверим: 3*9-15=9+3, 27-15=12, 12=12)

2) 7-3х=х+11
-3х-х=11-7
-4х=4
х=-1
Ответ: х= -1

3) 2(х+3)=х+13
2х+6=х+13
2х-х=13-6
х=7
Ответ: х=7

4) 4(5-х)=3х-1
20-4х=3х-1
-4х-3х=-1-20
-7х=-21
х=(-21):(-7)
х=3
Ответ: х=3

5) 3(х-2)=х+4
3х-6=х+4
3х-х=4+6
2х=10
х=5
Ответ: х=5

6) 5(х-1)=4х+3
5х-5=4х+3
5х-4х=3+5
х=8
Ответ: х=8


задание № 2

Запишем с помощью неравенств

1) Скорость автомашины больше 40 км/ч, но меньше 60 км/ч:
Скорость машины обозначим через v
40 км/час <v <60 км/час
2) в секции легкой атлетики в одной группе занимаются не меньше 12 учеников,но не больше 16.
Пусть у группе х учеников, тогда
12<х<16

Answer 2

1) To solve the equation 3x - 15 = x + 3, we need to isolate the variable x on one side of the equation.

First, let's simplify the equation by combining like terms.

3x - 15 = x + 3

To get rid of the x term on the right side, we can subtract x from both sides of the equation.

2x - 15 = 3

Next, we can isolate the term with x by adding 15 to both sides of the equation.

2x = 18

To solve for x, we can divide both sides of the equation by 2.

x = 9

So, the solution to the equation 3x - 15 = x + 3 is x = 9.

2) Moving on to the equation 7 - 3x = x + 11.

Let's simplify the equation by combining like terms.

7 - 3x = x + 11

To get rid of the x term on the right side, we can subtract x from both sides of the equation.

7 - 4x = 11

Next, we can isolate the term with x by subtracting 7 from both sides of the equation.

-4x = 4

To solve for x, we can divide both sides of the equation by -4.

x = -1

So, the solution to the equation 7 - 3x = x + 11 is x = -1.

3) Let's solve the equation 2(x + 3) = x + 13.

First, let's distribute the 2 to the terms inside the parentheses.

2x + 6 = x + 13

To isolate the term with x, we can subtract x from both sides of the equation.

2x - x + 6 = 13

Simplifying the equation further, we have x + 6 = 13.

To solve for x, we can subtract 6 from both sides of the equation.

x = 7

So, the solution to the equation 2(x + 3) = x + 13 is x = 7.

4) Moving on to the equation 4(5 - x) = 3x - 1 + 5.

First, let's distribute the 4 to the terms inside the parentheses.

20 - 4x = 3x + 4

To isolate the term with x, we can add 4x to both sides of the equation.

20 = 7x + 4

Next, we can subtract 4 from both sides of the equation.

16 = 7x

To solve for x, we can divide both sides of the equation by 7.

x = 16/7

So, the solution to the equation 4(5 - x) = 3x - 1 + 5 is x = 16/7.

5) Let's solve the equation 3(x - 2) = x + 4.

First, let's distribute the 3 to the terms inside the parentheses.

3x - 6 = x + 4

To isolate the term with x, we can subtract x from both sides of the equation.

2x - 6 = 4

Next, we can add 6 to both sides of the equation.

2x = 10

To solve for x, we can divide both sides of the equation by 2.

x = 5

So, the solution to the equation 3(x - 2) = x + 4 is x = 5.

6) Moving on to the equation 5(x - 1) = 4x + 3.

First, let's distribute the 5 to the terms inside the parentheses.

5x - 5 = 4x + 3

To isolate the term with x, we can subtract 4x from both sides of the equation.

5x - 4x - 5 = 3

Simplifying the equation further, we have x - 5 = 3.

To solve for x, we can add 5 to both sides of the equation.

x = 8

So, the solution to the equation 5(x - 1) = 4x + 3 is x = 8.

Writing inequalities

1) The speed of a car is greater than 40 km/h but less than 60 km/h can be written as:

40 km/h < speed of car < 60 km/h

2) In a section of athletics, the number of students in a group is not less than 12 but not greater than 16 can be written as:

12 <= number of students in the group <= 16