https://file.aiquickdraw.com/mathbot/file/1725379293134wwlc4sot.jpg

Let's solve the equation provided in the image:

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

### Step 1: Eliminate the fractions by finding a common denominator.
The denominators are 3 and 4. The least common denominator (LCD) is 12. Multiply every term in the equation by 12 to eliminate the fractions:

\[
12 \times \left(\frac{2x - 1}{3}\right) - 12 \times \left(\frac{3x - 1}{4}\right) = 12 \times (x + 1)
\]

This simplifies to:

\[
4(2x - 1) - 3(3x - 1) = 12(x + 1)
\]

### Step 2: Distribute and simplify.

Distribute the constants in each term:

\[
8x - 4 - (9x - 3) = 12x + 12
\]

Notice the subtraction of \(- (9x - 3)\):

\[
8x - 4 - 9x + 3 = 12x + 12
\]

Now, combine like terms:

\[
-x - 1 = 12x + 12
\]

### Step 3: Solve for \(x\).

Add \(x\) to both sides to start isolating \(x\):

\[
-1 = 13x + 12
\]

Next, subtract 12 from both sides:

\[
-13 = 13x
\]

Finally, divide by 13:

\[
x = -1
\]

### Solution:
The solution is \(x = -1\).

Would you like to ask any questions or need more details? Here are some related questions:

1. How do you determine the least common denominator?
2. Why is it necessary to distribute before combining like terms?
3. What steps would change if the equation included an additional term on the left side?
4. Can this equation be solved using a different method, like substitution?
5. What happens if you get a different solution when rechecking the steps?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

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

This page provides a detailed step-by-step solution to the linear equation (2x - 1)/3 - (3x - 1)/4 = x + 1. Learn how to find the least common denominator, apply the distributive property, and solve for x. Ideal for students in Grades 9-10.

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