Question

1) 5x - 3 (4x-1) = 7-2(7x+2) 2) 6(x-3) -3x=2x-4 3) В первом букете было в 4 раза меньше роз, чем во втором. Когда к первому букету добавили 15 роз, а к второму 3 розы, то в обоих букетах роз стало поровну. Сколько роз было в каждом букете первоначально?

Answer 1

Ответ:

1)5х-12х+3=7-14х-4

-7х+3=3-14х

-7х=-14х

-7х+14х=0

7х=0

Х=0:7

Х=0

2) 6х-18-3х=2х-4

3х-18=2х-4

3х-2х=-4+18

Х=14

Answer 2

Let's solve each equation step by step:

1. 5x - 3(4x-1) = 7 - 2(7x+2)

Expanding the brackets, we get: 5x - 12x + 3 = 7 - 14x - 4

Combining like terms: -7x + 3 = 7 - 14x - 4

Rearranging the equation: 7x - 14x = 7 - 4 - 3

-7x = 0

Dividing by -7: x = 0

Therefore, the solution is x = 0.

2. 6(x-3) - 3x = 2x - 4

Expanding the brackets, we get: 6x - 18 - 3x = 2x - 4

Combining like terms: 6x - 3x - 2x = 4 - 18

x - 2x = -14

Simplifying:

• x = -14

Multiplying by -1: x = 14

Therefore, the solution is x = 14.

3. Let's denote the number of roses in the first bouquet as x and in the second bouquet as y.

According to the given information, we have two equations:

Equation 1: x = (1/4)y (The first bouquet had four times fewer roses than the second bouquet)

Equation 2: x + 15 = y + 3 (When 15 roses were added to the first bouquet and 3 roses were added to the second bouquet, the total number of roses became equal)

Let's solve this system of equations:

Substituting Equation 1 into Equation 2: (1/4)y + 15 = y + 3

Multiplying through by 4 to eliminate the fraction: y + 60 = 4y + 12

Combining like terms: 3y = 48

Dividing by 3: y = 16

Substituting the value of y back into Equation 1: x = (1/4)(16) x = 4

Therefore, the initial number of roses in the first bouquet was 4, and the initial number of roses in the second bouquet was 16.