https://file.aiquickdraw.com/mathbot/file/1727303747041lqs0gpcd.jpg

The equation in the image is:

\[
\frac{1}{2}x + 3 - \frac{1}{4}x = 3 + \frac{1}{4}x
\]

Let's solve this step-by-step:

### Step 1: Simplify the equation
Move all the terms involving \(x\) to one side and constants to the other side.

\[
\frac{1}{2}x - \frac{1}{4}x - \frac{1}{4}x = 3 - 3
\]

### Step 2: Combine like terms
The left side has \(x\)-terms and the right side has constants. First, simplify the \(x\)-terms.

\[
\left( \frac{1}{2}x - \frac{1}{4}x - \frac{1}{4}x \right) = 0
\]

Combine the fractions:

\[
\frac{1}{2}x - 2\left(\frac{1}{4}x\right) = \frac{1}{2}x - \frac{2}{4}x = \frac{1}{2}x - \frac{1}{2}x = 0
\]

This gives:

\[
0 = 0
\]

### Step 3: Interpret the result
Since both sides of the equation simplify to \(0 = 0\), this indicates that the equation is **true for all values of \(x\)**. Therefore, the solution is that **any real number \(x\) is a solution**.

Would you like further details or have any questions?

---

Here are 5 related questions to explore:

1. What are the possible types of solutions in linear equations (one solution, no solution, or infinitely many solutions)?
2. How do we handle equations involving fractions with different denominators?
3. What is the geometric interpretation of equations that are true for all values of \(x\)?
4. How would the solution change if the equation had terms with \(x^2\) or other powers?
5. What strategies can be used to simplify equations with fractions?

**Tip:** When dealing with fractions in equations, it's often useful to clear them by multiplying through by the least common denominator (LCD).

Solve the equation: 1/2x + 3 - 1/4x = 3 + 1/4x

This step-by-step solution covers how to solve the linear equation with fractions: 1/2x + 3 - 1/4x = 3 + 1/4x. Learn the process of combining like terms and simplifying equations involving fractions. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation