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The given inequality is:

\[
1 - \frac{3x}{2} \leq \frac{5x + 14}{3} \leq \frac{9}{5}(2 - x)
\]

Let's break this into two inequalities and solve each part:

### 1. Solve \( 1 - \frac{3x}{2} \leq \frac{5x + 14}{3} \):

Step 1: Multiply through by 6 to eliminate the denominators:
\[
6 \left( 1 - \frac{3x}{2} \right) \leq 6 \left( \frac{5x + 14}{3} \right)
\]
This simplifies to:
\[
6 - 9x \leq 2(5x + 14)
\]
\[
6 - 9x \leq 10x + 28
\]

Step 2: Solve for \(x\):
\[
6 - 28 \leq 10x + 9x
\]
\[
-22 \leq 19x
\

Determine el conjunto solución de la siguiente inequación: 1 - (3x / 2) ≤ (5x + 14) / 3 ≤ (9 / 5)(2 - x).

Learn how to solve the compound inequality 1 - (3x / 2) ≤ (5x + 14) / 3 ≤ (9 / 5)(2 - x). This problem involves algebraic manipulation and solving inequalities step by step. Suitable for students in Grades 9-12.

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