Question

1)5x+(3x-7)=9 2)(5x-3)+(7x-4)=8-(15-11x) 3)2x+5=2(x+1)+11 4)5(3x+1,2)+x=6,8 5)6(x-1)=9,4-1,7x

Answer 1

1)5х+3х=9+7 3) 2х+5=2(х+1)+11  4) 15х+6+х=6,8 5)6х-6=9,4-1,7х
8х=16                2х+5=2х+2+11          15х+х=6,8-6     6х+1,7х=9,4+6
х=2                    2х+2х=2+11-5            16х=0,8             7,7х=15,4
                             4х=8                            х=2                      х=2
                               х=2

Answer 2

Давайте поочередно решим каждое уравнение.

1) \(5x + (3x - 7) = 9\)

Сначала раскроем скобки:

\[5x + 3x - 7 = 9\]

Теперь сложим коэффициенты при \(x\):

\[8x - 7 = 9\]

Теперь добавим 7 к обеим сторонам уравнения:

\[8x = 16\]

И, наконец, разделим на 8:

\[x = 2\]

2) \((5x - 3) + (7x - 4) = 8 - (15 - 11x)\)

Раскрываем скобки:

\[5x - 3 + 7x - 4 = 8 - 15 + 11x\]

Сложим коэффициенты при \(x\) и числа:

\[12x - 7 = -7 + 11x\]

Вычитаем \(11x\) из обеих сторон:

\[x - 7 = -7\]

Прибавляем 7 к обеим сторонам:

\[x = 0\]

3) \(2x + 5 = 2(x + 1) + 11\)

Раскрываем скобки:

\[2x + 5 = 2x + 2 + 11\]

Собираем коэффициенты при \(x\) и числа:

\[2x + 5 = 2x + 13\]

Вычитаем \(2x\) из обеих сторон:

\[5 = 13\]

Это уравнение не имеет решения, так как 5 не может быть равно 13. Таким образом, это уравнение является противоречивым.

4) \(5(3x + 1.2) + x = 6.8 + 5\)

Раскрываем скобки:

\[15x + 6 + x = 6.8 + 5\]

Собираем коэффициенты при \(x\) и числа:

\[16x + 6 = 11.8\]

Вычитаем 6 из обеих сторон:

\[16x = 5.8\]

Разделим на 16:

\[x = \frac{5.8}{16}\]

5) \(6(x - 1) = 9.4 - 1.7x\)

Раскрываем скобки:

\[6x - 6 = 9.4 - 1.7x\]

Собираем коэффициенты при \(x\) и числа:

\[6x + 1.7x = 9.4 + 6\]

Складываем:

\[7.7x = 15.4\]

Разделим на 7.7:

\[x = 2\]

Итак, решения уравнений:

1) \(x = 2\)

2) \(x = 0\)

3) Уравнение противоречиво, нет решений.

4) \(x = \frac{5.8}{16}\)

5) \(x = 2\)

Answer 3

Sure! Let's solve each of the equations step by step:

1) 5x + (3x - 7) = 9

To solve this equation, we first simplify the expression within the parentheses:

5x + 3x - 7 = 9

Combining like terms, we have:

8x - 7 = 9

Next, we isolate the variable by adding 7 to both sides:

8x - 7 + 7 = 9 + 7

This simplifies to:

8x = 16

Finally, we divide both sides by 8 to solve for x:

8x/8 = 16/8

x = 2

So the solution to the equation is x = 2.

2) (5x - 3) + (7x - 4) = 8 - (15 - 11x) + 3

We start by simplifying the expression within the parentheses:

5x - 3 + 7x - 4 = 8 - 15 + 11x + 3

Combining like terms, we get:

12x - 7 = -4 + 11x + 3

Next, we combine the x terms on one side and the constant terms on the other side:

12x - 11x = -4 + 3 + 7

This simplifies to:

x = 6

Therefore, the solution to the equation is x = 6.

3) 2x + 5 = 2(x + 1) + 11

We start by distributing the 2 to the terms inside the parentheses:

2x + 5 = 2x + 2 + 11

Combining like terms, we have:

2x + 5 = 2x + 13

Next, we can subtract 2x from both sides to isolate the constant term:

2x - 2x + 5 = 2x - 2x + 13

This simplifies to:

5 = 13

Since 5 is not equal to 13, there is no solution to this equation. The equation is inconsistent and does not have a valid solution.

4) 5(3x + 1.2) + x = 6.8

First, we distribute the 5 to the terms inside the parentheses:

15x + 6 + x = 6.8

Combining like terms, we have:

16x + 6 = 6.8

Next, we subtract 6 from both sides:

16x + 6 - 6 = 6.8 - 6

This simplifies to:

16x = 0.8

Finally, we divide both sides by 16 to solve for x:

16x/16 = 0.8/16

x = 0.05

Therefore, the solution to the equation is x = 0.05.

5) 6(x - 1) = 9.4 - 1.7x

First, we distribute the 6 to the term inside the parentheses:

6x - 6 = 9.4 - 1.7x

Next, we add 1.7x to both sides to isolate the x terms:

6x + 1.7x - 6 = 9.4 - 1.7x + 1.7x

This simplifies to:

7.7x - 6 = 9.4

Then, we add 6 to both sides:

7.7x - 6 + 6 = 9.4 + 6

This simplifies to:

7.7x = 15.4

Finally, we divide both sides by 7.7 to solve for x:

7.7x/7.7 = 15.4/7.7

x = 2

Therefore, the solution to the equation is x = 2.

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