Question

№1 (2,5-x)-(1,6-x)=6x РЕШИТЬ 4(x+3)+5x=30 0,2+(0,4x-1)=x+0,4 №2 Сева купил три ручки и карандаш за 12 рублей, а Полина купила две таких же ручки и блокнотик за 28 рублей. Оказалось, что ребята заплатили в кассу одинаковую сумму. Сколько стоит одна ручка? Ответ: №3 При каком значении параметра a: 1) Уравнение 15x - (4x - 9) = 11x + a имеет бесконечно много корней? 2) Уравнение 19 - 6x = (a - 5x) - x не имеет корней? №4 При каких значениях переменной значения выражений 32x - 4 и 15x + 6 равны? №5 Сколько корней имеет уравнение 5x-(10-x) = 6x - 10? Напишите полное решение и ответ. №6 При каких значениях переменной x значения выражений 32x - 4 и 15x + 6 равны? Напишите полное решение и ответ. №7 При каком значении b уравнение 5x+b=6(x-4)-x не имеет корней? Напишите полное решение и ответ.

Answer 1

1. х=0.15
х=2
х=2

2.Ручка стоит16 рублей

3. 1)а9
2)а≥20; а≤-20

4.х= 10/17

5. (Фото1)

6. Аналогично 4.(фото 2)

7.(фото 3)

Answer 2

№1: To solve the equation (2.5 - x) - (1.6 - x) = 6x + 4(x + 3) + 5x = 30, we need to simplify it step by step.

Step 1: Simplify the equation (2.5 - x) - (1.6 - x): 2.5 - x - 1.6 + x = 6x + 4(x + 3) + 5x = 30

Step 2: Combine like terms on both sides of the equation: (2.5 - 1.6) - (x - x) = 6x + 4x + 12 + 5x = 30 0.9 = 15x + 12 + 9x = 30

Step 3: Simplify the equation further: 0.9 = 24x + 12 = 30

Step 4: Subtract 12 from both sides of the equation: 0.9 - 12 = 24x = 18

Step 5: Divide both sides of the equation by 24: -11.1 = x

Therefore, the solution to the equation (2.5 - x) - (1.6 - x) = 6x + 4(x + 3) + 5x = 30 is x = -11.1.

№2: To find the cost of one pen, we can set up an equation using the given information.

Let's assume the cost of one pen is x rubles.

According to the given information: Seva bought three pens and a pencil for 12 rubles. Polina bought two pens and a notebook for 28 rubles.

We can set up the following equation: 3x + x = 12 2x + 28 = 28

Simplifying the equations: 4x = 12 2x = 16

Solving for x: x = 12/4 x = 3

Therefore, the cost of one pen is 3 rubles.

№3: To determine the values of the parameter "a" for which the equation 15x - (4x - 9) = 11x + a has infinitely many solutions, we need to simplify the equation and analyze the coefficients.

Step 1: Simplify the equation: 15x - 4x + 9 = 11x + a

Step 2: Combine like terms on both sides of the equation: 11x + 9 = 11x + a

Step 3: Cancel out the 11x terms by subtracting 11x from both sides of the equation: 9 = a

Therefore, the equation 15x - (4x - 9) = 11x + a has infinitely many solutions when a = 9.

To determine the values of the parameter "a" for which the equation 19 - 6x = (a - 5x) - x has no solutions, we need to simplify the equation and analyze the coefficients.

Step 1: Simplify the equation: 19 - 6x = a - 5x - x

Step 2: Combine like terms on both sides of the equation: 19 - 6x = a - 6x

Step 3: Cancel out the -6x terms by subtracting an equal number from both sides of the equation: 19 = a

Therefore, the equation 19 - 6x = (a - 5x) - x has no solutions when a = 19.

№4: To find the values of the variable for which the expressions 32x - 4 and 15x + 6 are equal, we need to set up an equation and solve for x.

Set up the equation: 32x - 4 = 15x + 6

Simplify the equation: 32x - 15x = 6 + 4 17x = 10

Divide both sides of the equation by 17: x = 10/17

Therefore, the values of the variable for which the expressions 32x - 4 and 15x + 6 are equal is x = 10/17.

№5: To determine the number of solutions for the equation 5x - (10 - x) = 6x - 10, we need to simplify the equation and analyze the coefficients.

Step 1: Simplify the equation: 5x - 10 + x = 6x - 10

Step 2: Combine like terms on both sides of the equation: 6x - 10 = 6x - 10

Step 3: Subtract 6x from both sides of the equation: -10 = -10

The equation -10 = -10 is always true, which means that it holds for all values of x. Therefore, the equation 5x - (10 - x) = 6x - 10 has infinitely many solutions.

№6: To find the values of the variable for which the expressions 32x - 4 and 15x + 6 are equal, we need to set up an equation and solve for x.

Set up the equation: 32x - 4 = 15x + 6

Simplify the equation: 32x - 15x = 6 + 4 17x = 10

Divide both sides of the equation by 17: x = 10/17

Therefore, the values of the variable for which the expressions 32x - 4 and 15x + 6 are equal is x = 10/17.

№7: To find the value of b for which the equation 5x + b = 6(x - 4) - x has no solutions, we need to simplify the equation and analyze the coefficients.

Step 1: Simplify the equation: 5x + b = 6x - 24 - x

Step 2: Combine like terms on both sides of the equation: 5x + b = 5x - 24

Step 3: Subtract 5x from both sides of the equation: b = -24

Therefore, the equation 5x + b = 6(x - 4) - x has no solutions when b = -24.