Let's solve the given expression step by step:

The expression is:

\[
27 - 7 \times \left\langle -7(x - 4) \right\rangle
\]

### Step 1: Simplify the multiplication inside the brackets.

First, distribute the \(-7\) to the terms inside the parentheses \((x - 4)\):

\[
-7(x - 4) = -7x + 28
\]

### Step 2: Multiply by 7.

Now, multiply \(7\) by the result:

\[
7 \times (-7x + 28) = -49x + 196
\]

### Step 3: Simplify the overall expression.

Now substitute this back into the original expression:

\[
27 - (-49x + 196)
\]

This simplifies to:

\[
27 + 49x - 196
\]

### Step 4: Combine like terms.

Combine the constant terms \(27\) and \(-196\):

\[
49x - 169
\]

### Final Answer:

\[
49x - 169
\]

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Would you like a more detailed breakdown, or do you have any questions?

Here are 5 related questions:
1. How do you distribute negative numbers across parentheses?
2. What are some common mistakes when working with negative signs in algebra?
3. How can we solve \(49x - 169 = 0\)?
4. What happens if the original equation had different constants?
5. How does factoring work in simplifying expressions?

**Tip:** Always simplify inside parentheses first before multiplying to avoid errors.

This problem demonstrates how to simplify the expression 27 - 7 × -7(x - 4) using the distributive property and combining like terms. Ideal for students in Grades 7-9, it covers fundamental algebraic concepts such as distribution and simplification.

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