https://file.aiquickdraw.com/mathbot/file/1725652670317f50ni4xn.jpg

It looks like you've uploaded an image of a math problem. The equation shown in the image is:

\[
\frac{x}{2} - \frac{x-2}{3} = (x+1) - 5
\]

Let me solve it step-by-step:

### Step 1: Simplify the equation
We need to eliminate the fractions first by finding a common denominator between 2 and 3. The least common denominator (LCD) is 6.

So, multiply the entire equation by 6:

\[
6 \times \left(\frac{x}{2}\right) - 6 \times \left(\frac{x-2}{3}\right) = 6 \times ((x+1) - 5)
\]

This simplifies to:

\[
3x - 2(x - 2) = 6(x+1 - 5)
\]

### Step 2: Distribute
Distribute the constants across the terms:

\[
3x - 2(x - 2) = 6(x - 4)
\]

Distribute further:

\[
3x - 2x + 4 = 6x - 24
\]

### Step 3: Combine like terms
Simplify the terms:

\[
x + 4 = 6x - 24
\]

### Step 4: Solve for \(x\)
Move all terms involving \(x\) to one side and constant terms to the other:

\[
4 + 24 = 6x - x
\]

\[
28 = 5x
\]

Now, solve for \(x\):

\[
x = \frac{28}{5}
\]

So, the solution to the equation is:

\[
x = \frac{28}{5}
\]

Do you want further details or have any questions?

Here are five related questions to expand your understanding:
1. How would you solve the equation if the fractions had different denominators, such as 4 and 5?
2. What are the steps for solving a quadratic equation?
3. Can you solve an equation with multiple variables using substitution or elimination?
4. What happens when an equation has no solution or infinitely many solutions?
5. How would you approach solving equations with absolute values?

**Tip**: Always aim to eliminate fractions by finding a common denominator early in the process. This simplifies the work and reduces potential errors.

Solve the equation: x/2 - (x-2)/3 = (x+1) - 5

Learn how to solve the linear equation x/2 - (x-2)/3 = (x+1) - 5 step-by-step. This problem covers essential algebraic concepts such as eliminating fractions and combining like terms, suitable for students in Grades 8-10.

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