Solve the compound inequality. $$ 2 u-2 \leq 10 \text { or } 4 u-3 \leq-15 $$ Write the solution in interval notation. If there is no solution, enter $$ \varnothing $$.

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To solve the compound inequality:

$$
2u - 2 \leq 10 \quad \text{or} \quad 4u - 3 \leq -15
$$

We solve each inequality separately:

1. **First Inequality:**

$$
2u - 2 \leq 10
$$

Add 2 to both sides:

$$
2u \leq 12
$$

Divide by 2:

$$
u \leq 6
$$

2. **Second Inequality:**

$$
4u - 3 \leq -15
$$

Add 3 to both sides:

$$
4u \leq -12
$$

Divide by 4:

$$
u \leq -3
$$

**Combining the Solutions:**

The compound inequality uses "or," which means we take the union of the two solutions:

$$
u \leq 6 \quad \text{or} \quad u \leq -3
$$

Since $$ u \leq 6 $$ already includes all values where $$ u \leq -3 $$, the overall solution is:

$$
u \leq 6
$$

**Interval Notation:**

$$
(-\infty, 6]
$$

**Final Answer:**

$$\boxed{\,(-\infty,\ 6\,]\,}$$
The solution is all real numbers less than or equal to 6, written as $$ (-\infty, 6] $$.

Solve the compound inequality.

Write the solution in interval notation.
If there is no solution, enter .

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