Question

COP «Линейное уравнение с одной переменной 83 1. Решите уравнения: 1 вариант 1) 9x-7 = 6x + 14; 2) 4x - (7x + 5) = 10 (36) 2. Решите уравнения: 1) 3 (4-2 x) + 8 = - 2x + 4. 2) 7x-3(2x + 1) = 2x + 3 (46) 3. Решите уравнения с модулем: 1) | 10x+ 6 = 4; 2) |2x - 5+12=37 (46) 4. Решите задачу, составив уравнение: В первом мешке было в 4 раза больше сахара, чем во втором. Когда из первого мешка взяли 10 кг сахара, а во второй досыпали 5 кг, то в мешках стало поровну сахара. Сколько килограммов сахара было в каждом мешке сначала? (36)​

Answer 1

Ответ:

Ответ на фото Удачи!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 2

Solving Linear Equations with One Variable

1. Equation 1: 9x - 7 = 6x + 14 To solve this equation, we need to isolate the variable x on one side of the equation. We can do this by performing algebraic operations to both sides of the equation. Here's the step-by-step solution:

   9x - 7 = 6x + 14
   Subtract 6x from both sides:
   9x - 6x - 7 = 6x - 6x + 14
   Simplify:
   3x - 7 = 14
   Add 7 to both sides:
   3x - 7 + 7 = 14 + 7
   Simplify:
   3x = 21
   Divide both sides by 3:
   3x/3 = 21/3
   Simplify:
   x = 7
   

Therefore, the solution to the equation 9x - 7 = 6x + 14 is x = 7.

2. Equation 2: 4x - (7x + 5) = 10 + 36 To solve this equation, we need to simplify the expression inside the parentheses first. Here's the step-by-step solution:

   4x - (7x + 5) = 10 + 36
   Distribute the negative sign to the terms inside the parentheses:
   4x - 7x - 5 = 10 + 36
   Simplify:
   -3x - 5 = 46
   Add 5 to both sides:
   -3x - 5 + 5 = 46 + 5
   Simplify:
   -3x = 51
   Divide both sides by -3:
   -3x/-3 = 51/-3
   Simplify:
   x = -17
   

Therefore, the solution to the equation 4x - (7x + 5) = 10 + 36 is x = -17.

Solving Equations with Absolute Value

3. Equation 3: |10x + 6| = 4 To solve this equation, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative. Here's the step-by-step solution:

Case 1: 10x + 6 > 0 ``` 10x + 6 = 4 Subtract 6 from both sides: 10x + 6 - 6 = 4 - 6 Simplify: 10x = -2 Divide both sides by 10: 10x/10 = -2/10 Simplify: x = -0.2 ```

Case 2: 10x + 6 < 0 ``` -(10x + 6) = 4 Distribute the negative sign to the expression inside the parentheses: -10x - 6 = 4 Add 6 to both sides: -10x - 6 + 6 = 4 + 6 Simplify: -10x = 10 Divide both sides by -10: -10x/-10 = 10/-10 Simplify: x = -1 ```

Therefore, the solutions to the equation |10x + 6| = 4 are x = -0.2 and x = -1.

Solving Word Problems using Equations

4. Word Problem: In the first bag, there was 4 times more sugar than in the second bag. When 10 kg of sugar was taken from the first bag and 5 kg was added to the second bag, the amount of sugar in the bags became equal. How many kilograms of sugar were initially in each bag? Let's assume the amount of sugar in the second bag is x kg. According to the problem, the amount of sugar in the first bag is 4 times more, which means it is 4x kg.

After taking 10 kg from the first bag and adding 5 kg to the second bag, the amounts become equal. We can set up the following equation:

   4x - 10 = x + 5
   

To solve this equation, we can perform algebraic operations to isolate the variable x:

   4x - x = 5 + 10
   3x = 15
   x = 5
   

Therefore, initially, there were 20 kg of sugar in the first bag and 5 kg of sugar in the second bag.

I hope this helps! Let me know if you have any further questions.