Let's simplify the given algebraic expression step by step:

$(7x - 9) - 6(2x + 1)$

Step 1: Distribute $-6$ inside the parentheses

Multiply $-6$ by both terms inside the parentheses:

$(7x - 9) - 12x - 6$

Step 2: Combine like terms

Combine the $x$-terms:

$7x - 12x = -5x$

Combine the constant terms:

$-9 - 6 = -15$

Final Expression:

$-5x - 15$

This is the simplified form.

Would you like more explanation or have any questions?

Here are five related problems for practice:

1. $(3x + 4) - 5(2x - 1)$
2. $(8y - 7) - 3(y + 2)$
3. $2(5x - 3) - 4(x + 6)$
4. $9a - 4(2a + 5)$
5. $6m - (3m + 12)$

Tip: Always distribute negative signs carefully when simplifying expressions!