https://r2.erweima.ai/mathbot/image/1726306558495ddzsrm0b.jpg

Let's solve the equation \( 43 = 7 + 3(5 + 2v) \).

### Step-by-Step Solution:

1. **Distribute the 3 over the terms inside the parentheses**:
   \[
   43 = 7 + 3(5 + 2v)
   \]
   becomes:
   \[
   43 = 7 + 15 + 6v
   \]

2. **Simplify the right-hand side** by combining the constants \( 7 \) and \( 15 \):
   \[
   43 = 22 + 6v
   \]

3. **Isolate the \( v \)-term** by subtracting 22 from both sides:
   \[
   43 - 22 = 6v
   \]
   which simplifies to:
   \[
   21 = 6v
   \]

4. **Solve for \( v \)** by dividing both sides by 6:
   \[
   v = \frac{21}{6} = 3.5
   \]

### Final Answer:
\[
v = 3.5
\]

Let me know if you'd like more details or further clarification! Here are five related questions to extend your practice:

1. How would you solve \( 60 = 8 + 4(3 + 2x) \)?
2. What if the equation were \( 50 = 5 + 2(10 + 3y) \)?
3. Can you solve \( 35 = 6 + 2(7 + v) \)?
4. How would you distribute and solve \( 56 = 10 + 4(5 + x) \)?
5. What happens when the equation is \( 100 = 20 + 10(2 + 3v) \)?

**Tip:** Always simplify expressions inside parentheses first, then distribute and solve step by step!

Learn how to solve the linear equation 43 = 7 + 3(5 + 2v) using distributive property and basic algebraic steps. This problem covers key algebraic concepts, including the distributive property and solving linear equations. Suitable for students in Grades 7-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation