Solve for x.

5x-2(x+1)=(1)/(4)

Enter your answer as a fraction in simplest form in the box.

x=

Let's solve the equation step by step:

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

### Step 1: Distribute the \(-2\) to the terms inside the parentheses.
\[
5x - 2x - 2 = \frac{1}{4}
\]

### Step 2: Combine like terms on the left side.
\[
(5x - 2x) - 2 = \frac{1}{4}
\]
\[
3x - 2 = \frac{1}{4}
\]

### Step 3: Add 2 to both sides to isolate the \(3x\) term.
\[
3x = \frac{1}{4} + 2
\]
Since 2 can be written as \(\frac{8}{4}\), this becomes:
\[
3x = \frac{1}{4} + \frac{8}{4}
\]
\[
3x = \frac{9}{4}
\]

### Step 4: Divide both sides by 3 to solve for \(x\).
\[
x = \frac{9}{4} \div 3 = \frac{9}{4} \times \frac{1}{3} = \frac{9}{12}
\]

### Step 5: Simplify the fraction.
\[
x = \frac{3}{4}
\]

Thus, the solution is:
\[
x = \frac{3}{4}
\]

Would you like more details on any step? Here are a few questions to explore the topic further:

1. How do you simplify fractions like \(\frac{9}{12}\)?
2. What happens if you subtract \(\frac{1}{4}\) instead of adding it?
3. How can you check if \(\frac{3}{4}\) is the correct solution?
4. What are some other methods for solving linear equations?
5. How does distributing work in other contexts of algebra?

**Tip:** Always simplify fractions at the end of solving equations for the cleanest answer.

Solve for x. 5x - 2(x + 1) = 1/4. Enter your answer as a fraction in simplest form in the box. x =

Discover how to solve the linear equation 5x - 2(x + 1) = 1/4 step by step, including distributing, combining like terms, and solving for x as a fraction. Ideal for students in Grades 6-8, this problem emphasizes algebraic simplification and fraction operations.

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