We are given the equation:

\[
\frac{x+1}{2} - 3 = \frac{1+x}{3}
\]

### Step 1: Eliminate fractions by finding a common denominator.
The least common denominator (LCD) of 2 and 3 is 6. Multiply both sides of the equation by 6:

\[
6 \times \left( \frac{x+1}{2} - 3 \right) = 6 \times \frac{1+x}{3}
\]

This simplifies to:

\[
3(x+1) - 18 = 2(1+x)
\]

### Step 2: Expand both sides.
Expand the terms inside the parentheses:

\[
3x + 3 - 18 = 2 + 2x
\]

Simplify further:

\[
3x - 15 = 2 + 2x
\]

### Step 3: Move all terms involving \(x\) to one side.
Subtract \(2x\) from both sides:

\[
x - 15 = 2
\]

### Step 4: Solve for \(x\).
Add 15 to both sides:

\[
x = 17
\]

So, the solution is \(x = 17\).

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

Here are 5 related questions:
1. How do you handle equations with variables on both sides?
2. Can you explain the concept of least common denominator (LCD)?
3. What is the importance of simplifying an equation before solving?
4. How do you check if your solution is correct?
5. How can you solve similar equations with fractions?

**Tip:** Always simplify your equation step by step to avoid errors when working with fractions and variables.

This article provides a step-by-step solution to the equation x+1 /2 - 3 = 1+x /3. Learn how to handle fractions, find the least common denominator (LCD), and solve for x. Suitable for students in Grades 8-10, covering key algebraic concepts such as solving linear equations with fractions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation