Question

Найдите целые решения системы неравенств.(3х - 12 >< 4х – 17 – 2x < 10 — 3х​

Answer 1

Ответ:

1) 7 - 2x ≤ 10 - 3х;

Перенесем свободный член вправо:

3х - 2x ≤ 10 - 7;

x1 ≤ 3;

х1 ∈ (- ∞; 3];

2) 3x + 12 > 4х - 1;

Перенесем свободный член вправо:

3x - 4х > - 12 - 1;

- x > - 13;

Разделим на ( - 1), изменив знак неравенства:

x < - 13 / ( - 1);

x2 < 13;

х2 ∈ (- ∞; 13);

Нанесем общие значения на координатную ось:

///////////////

---•(3)--- °(13)---

/////

х ∈ (- ∞; 3];

Ответ: х ∈ (- ∞; 3].

Answer 2

Solving the Inequality System

To solve the inequality system 3x - 12 < 4x - 17 - 2x < 10, we can break it down into two separate inequalities and solve for the values of x that satisfy both inequalities.

The given inequality system can be split into two separate inequalities: 1. 3x - 12 < 4x - 17 - 2x 2. 4x - 17 - 2x < 10

Solving the First Inequality

For the first inequality 3x - 12 < 4x - 17 - 2x, we can simplify it as follows: 3x - 12 < 4x - 17 - 2x x - 12 < 4x - 17 -12 + 17 < 4x - x 5 < 3x 5/3 < x

So, the solution to the first inequality is x > 5/3.

Solving the Second Inequality

For the second inequality 4x - 17 - 2x < 10, we can simplify it as follows: 4x - 17 - 2x < 10 2x - 17 < 10 2x < 27 x < 27/2

So, the solution to the second inequality is x < 27/2.

Combining the Solutions

By combining the solutions of both inequalities, we get: 5/3 < x < 27/2

Therefore, the solution to the given inequality system 3x - 12 < 4x - 17 - 2x < 10 is 5/3 < x < 27/2.