`5 (2x - 7 ) -3 ( 2x + 3 ) le 0, 2x + 19 le 6x + 47`

Explanation

To solve the inequalities step by step, let's break down the given inequalities one by one.

### Given Inequalities:
1. \( 5(2x - 7) - 3(2x + 3) \leq 0 \)
2. \( 2x + 19 \leq 6x + 47 \)

### Step 1: Solve the first inequality
Start with the first inequality:

\[ 5(2x - 7) - 3(2x + 3) \leq 0 \]

Distributing the terms:

\[ 10x - 35 - 6x - 9 \leq 0 \]

Combine like terms:

\[ (10x - 6x) + (-35 - 9) \leq 0 \]

This simplifies to:

\[ 4x - 44 \leq 0 \]

### Step 2: Isolate \(x\)
Now, add 44 to both sides:

\[ 4x \leq 44 \]

Now, divide both sides by 4:

\[ x \leq 11 \]

### Step 3: Solve the second inequality
Now, let's solve the second inequality:

\[ 2x + 19 \leq 6x + 47 \]

Subtract \(2x\) from both sides:

\[ 19 \leq 4x + 47 \]

Now, subtract 47 from both sides:

\[ 19 - 47 \leq 4x \]

This simplifies to:

\[ -28 \leq 4x \]

### Step 4: Isolate \(x\)
Now, divide both sides by 4:

\[ -7 \leq x \quad \text{or} \quad x \geq -7 \]

### Step 5: Combine the results
We now have two conditions:

1. \( x \leq 11 \)
2. \( x \geq -7 \)

### Step 6: Write the final solution
Combining these inequalities, we find:

\[ -7 \leq x \leq 11 \]

This means \( x \) belongs to the interval:

\[ x \in [-7, 11] \]