Let's solve the equation step by step:

Given equation:
\[
6 + 5(p - 1) = 46
\]

### Step 1: Distribute the 5 to terms inside the parentheses.
\[
6 + 5p - 5 = 46
\]

### Step 2: Combine like terms.
\[
(6 - 5) + 5p = 46
\]
\[
1 + 5p = 46
\]

### Step 3: Subtract 1 from both sides.
\[
5p = 46 - 1
\]
\[
5p = 45
\]

### Step 4: Divide both sides by 5 to solve for \( p \).
\[
p = \frac{45}{5}
\]
\[
p = 9
\]

Thus, the solution is \( p = 9 \).

Would you like further details or have any questions?

Here are 5 related questions:
1. What would happen if the equation was \( 6 + 5(p - 2) = 46 \)?
2. Can you solve \( 6 + 4(p - 1) = 34 \)?
3. What happens if you subtract 6 from both sides of the original equation at the start?
4. How can we check if our solution is correct?
5. What if the equation was \( 6 + 5(p + 1) = 46 \)?

**Tip**: Always distribute and combine like terms first when solving equations with parentheses!

Learn how to solve the linear equation 6 + 5(p-1) = 46 with a detailed step-by-step solution. This problem covers key algebra concepts like the distributive property and linear equations. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation