Simplify the expression

15 -6(2m + 1) - 34 +4m

Let's simplify the expression step by step:

**Given Expression:**
\[
15 - 6(2m + 1) - 34 + 4m
\]

### Step 1: Distribute the \(-6\) across the terms inside the parentheses.
\[
-6 \times 2m = -12m, \quad -6 \times 1 = -6
\]
So, the expression becomes:
\[
15 - 12m - 6 - 34 + 4m
\]

### Step 2: Combine like terms.
- Combine the constant terms: \( 15 - 6 - 34 \)
\[
15 - 6 = 9, \quad 9 - 34 = -25
\]
So, the constant term is \(-25\).

- Combine the \( m \) terms: \(-12m + 4m\)
\[
-12m + 4m = -8m
\]

### Final Simplified Expression:
\[
-8m - 25
\]

The simplified expression is \( \boxed{-8m - 25} \).

Would you like more details, or do you have any other questions?

Here are 8 related questions that expand on this problem:
1. How would the expression change if the sign of \(6(2m + 1)\) were positive instead of negative?
2. How do you check if your simplification of an algebraic expression is correct?
3. What happens to the expression if the term \(4m\) is negative?
4. Can you factorize the expression after simplifying it?
5. How would this expression be represented graphically?
6. What are some common mistakes to avoid when simplifying expressions with multiple terms?
7. Can you rewrite the expression in a different form, such as by factoring out common terms?
8. What is the role of the distributive property in simplifying algebraic expressions?

**Tip:** When simplifying expressions, carefully track the signs and coefficients, especially during distribution and combining like terms.

Learn how to simplify the expression 15 - 6(2m + 1) - 34 + 4m step-by-step with a detailed solution. This problem covers key algebraic concepts including the distributive property and combining like terms. Suitable for students in Grades 7-9.

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