Question

1/4(3х-11)-3-5х/8=х+6/2

Answer 1

Ответ:

х = 7

Объяснение:

Решаем линейное уравнение с одной переменной (3х - 11)/4 - (3 - 5х)/8 = (х + 6)/2, используя тождественные преобразования.

Умножим на 8 обе части уравнения, тем самым избавимся от знака дроби в обеих частях уравнения.

2(3х - 11) - (3 - 5х) = 4(х + 6);

Открываем скобки в обеих частях уравнения:

6х - 22 - 3 + 5х = 4х + 24;

6х + 5х - 4х = 24 + 22 + 3;

Приведем подобные слагаемые в обеих частях уравнения:

7х = 49;

Разделим на 7 обе части уравнения, получим:

х = 49 : 7;

х = 7.

Ответ: х = 7 корень уравнения.

Answer 2

To solve the equation 1/4(3x - 11) - 3 - 5x/8 = x + 6/2, you can follow these steps:

Step 1: Distribute the 1/4 on the left side of the equation: (1/4)(3x) - (1/4)(11) - 3 - 5x/8 = x + 3

This simplifies to: (3x/4) - (11/4) - 3 - 5x/8 = x + 3

Step 2: Combine like terms on the left side of the equation. To do this, find a common denominator for the fractions:

(3x/4) - (11/4) - (3 * 4/4) - (5x/8) = x + 3

This gives you:

(3x/4 - 11/4 - 12/4 - 5x/8) = x + 3

Step 3: Now, combine the fractions on the left side:

(3x - 11 - 12 - 10x) / 8 = x + 3

Step 4: To eliminate the fraction, you can multiply both sides of the equation by 8:

8(3x - 11 - 12 - 10x) / 8 = 8(x + 3)

This simplifies to:

3x - 11 - 12 - 10x = 8x + 24

Step 5: Now, combine like terms on both sides of the equation:

(3x - 10x) - 11 - 12 = 8x + 24

-7x - 23 = 8x + 24

Step 6: Move the variable terms to one side and the constant terms to the other side. You can do this by adding 7x and 23 to both sides:

-7x - 7x - 23 + 23 = 8x + 7x + 24 + 23

-14x = 15x + 47

Step 7: To isolate x, subtract 15x from both sides:

-14x - 15x = 15x - 15x + 47

-29x = 47

Step 8: Finally, divide both sides by -29 to solve for x:

(-29x) / (-29) = 47 / (-29)

x = -47/29

So, the solution to the equation is:

x = -47/29