minus, 5, left parenthesis, 6, m, plus, 3, right parenthesis, minus, 7, left parenthesis, minus, 7, m, plus, 7, right parenthesis−5(6m+3)−7(−7m+7)

Let's simplify the expression:

\[
-5(6m + 3) - 7(-7m + 7)
\]

### Step 1: Distribute each term
1. Distribute \(-5\) to both terms inside the first parentheses:
   \[
   -5 \cdot 6m = -30m \quad \text{and} \quad -5 \cdot 3 = -15
   \]
   So, \(-5(6m + 3) = -30m - 15\).

2. Distribute \(-7\) to both terms inside the second parentheses:
   \[
   -7 \cdot (-7m) = 49m \quad \text{and} \quad -7 \cdot 7 = -49
   \]
   So, \(-7(-7m + 7) = 49m - 49\).

### Step 2: Combine like terms
Now we have:
\[
-30m - 15 + 49m - 49
\]

Combine the \(m\) terms and the constant terms:
\[
(-30m + 49m) + (-15 - 49) = 19m - 64
\]

### Final Answer:
\[
19m - 64
\]

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

Here are some additional practice questions based on this topic:

1. Simplify: \(-3(4x + 5) + 6(2x - 7)\).
2. Simplify: \(7(5y - 2) - 4(3y + 9)\).
3. Evaluate: \(-8(a + 3) - 6(-2a + 5)\).
4. Simplify: \(2(9n - 4) - 5(3n + 8)\).
5. Simplify: \(-10(2x - 1) + 15(x + 3)\).

**Tip:** When distributing a negative sign, remember it reverses the sign of each term inside the parentheses.

Explore how to simplify the algebraic expression -5(6m + 3) - 7(-7m + 7) using the distributive property and combining like terms. This detailed solution is ideal for middle school students (Grades 7-8) learning to work with variable expressions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation