We will solve the equation step by step:

### Given equation:
\[
2x + \frac{2}{4} = \frac{1}{2} + \frac{x}{5}
\]

### Step 1: Simplify the fractions
\[
\frac{2}{4} = \frac{1}{2}
\]
Substitute this into the equation:
\[
2x + \frac{1}{2} = \frac{1}{2} + \frac{x}{5}
\]

### Step 2: Subtract \(\frac{1}{2}\) from both sides
\[
2x = \frac{x}{5}
\]

### Step 3: Eliminate the fraction by multiplying the entire equation by 5
\[
5(2x) = 5\left(\frac{x}{5}\right)
\]
\[
10x = x
\]

### Step 4: Subtract \(x\) from both sides
\[
10x - x = 0
\]
\[
9x = 0
\]

### Step 5: Solve for \(x\)
\[
x = 0
\]

Thus, the solution to the equation is:
\[
x = 0
\]

Would you like further details or have any questions?

Here are five related questions:
1. What happens if \(x\) is multiplied by a constant?
2. How do you handle equations with more complex fractions?
3. How do you check if a solution to an equation is correct?
4. How can you solve equations with variables on both sides?
5. What is the effect of dividing an equation by a variable?

**Tip:** Always double-check your solutions by substituting them back into the original equation.

This page provides a detailed solution to the linear equation 2x + 2/4 = 1/2 + x/5. The step-by-step process involves simplifying fractions and solving for x. The problem highlights important algebraic concepts like handling fractions and variables on both sides, 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