Find the value of x in this equation.
__
3
4
(6x + 1) − 3x = __
1
4
(2x − 1)

The equation you've provided is:

\[
\frac{3}{4}(6x + 1) - 3x = \frac{1}{4}(2x - 1)
\]

To solve for \(x\), let's go step by step:

### Step 1: Eliminate the fractions
To eliminate the fractions, multiply the entire equation by 4 (the least common denominator):

\[
4 \times \left(\frac{3}{4}(6x + 1) - 3x\right) = 4 \times \frac{1}{4}(2x - 1)
\]

This simplifies to:

\[
3(6x + 1) - 12x = 2x - 1
\]

### Step 2: Distribute the terms
Distribute 3 on the left-hand side:

\[
18x + 3 - 12x = 2x - 1
\]

### Step 3: Combine like terms
On the left-hand side, combine \(18x\) and \(-12x\):

\[
6x + 3 = 2x - 1
\]

### Step 4: Move variables to one side
Subtract \(2x\) from both sides:

\[
6x - 2x + 3 = -1
\]

This simplifies to:

\[
4x + 3 = -1
\]

### Step 5: Solve for \(x\)
Subtract 3 from both sides:

\[
4x = -4
\]

Finally, divide by 4:

\[
x = -1
\]

### Solution:
The value of \(x\) is \(-1\).

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

---

Here are 5 related questions to expand your understanding:

1. How do you handle equations with different denominators?
2. What happens if there are more terms involving \(x\) on both sides?
3. How do you solve equations where \(x\) appears inside parentheses and fractions?
4. How do you check if your solution is correct by substituting the value of \(x\) back into the equation?
5. What is the role of distributing and combining like terms in solving linear equations?

**Tip:** Always start by eliminating fractions when possible, as it simplifies the equation and makes solving easier.

Find the value of x in this equation.
(3/4)(6x + 1) − 3x = (1/4)(2x − 1)

Learn how to solve the linear equation (3/4)(6x + 1) − 3x = (1/4)(2x − 1) using step-by-step techniques. This algebra problem covers key concepts such as distribution, combining like terms, and solving linear equations with fractions. Ideal for students in Grades 8-10.

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