Let's solve the equation \( 2 + 5(1 - 7k) = 147 \).

### Step 1: Distribute the 5
Distribute the 5 across the terms inside the parentheses:
\[
2 + 5 \cdot 1 - 5 \cdot 7k = 147
\]
\[
2 + 5 - 35k = 147
\]

### Step 2: Combine like terms
Now, combine the constants on the left-hand side:
\[
7 - 35k = 147
\]

### Step 3: Isolate the variable term
Subtract 7 from both sides to move the constant to the right:
\[
-35k = 147 - 7
\]
\[
-35k = 140
\]

### Step 4: Solve for \( k \)
Divide both sides by -35:
\[
k = \frac{140}{-35}
\]
\[
k = -4
\]

### Final Answer:
\[
k = -4
\]

Would you like more details or have any questions?

Here are five related questions:
1. How would the solution change if the constant term were different?
2. What happens when there are multiple variables in such equations?
3. How do you solve similar equations with fractions?
4. What is the impact of negative signs on both sides of the equation?
5. How would you verify the solution by substitution?

**Tip**: Always check your solution by substituting it back into the original equation to avoid mistakes!

Learn how to solve the linear equation 2 + 5(1 - 7k) = 147. This step-by-step guide covers the distributive property, isolating variables, and combining like terms. Perfect for students in Grades 8-10 looking to strengthen their algebra skills.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation