Add:
`7x, -3x, 5x, -x, -2x`

Answer

To solve the problem of adding the algebraic expressions \(7x, -3x, 5x, -x, -2x\), we can follow these steps:

### Step 1: Write down the expression
We start with the expression:
\[ 7x + (-3x) + 5x + (-x) + (-2x) \]

### Step 2: Combine like terms
Next, we can group the positive and negative terms together. The positive terms are \(7x\) and \(5x\), and the negative terms are \(-3x\), \(-x\), and \(-2x\).

### Step 3: Add the positive terms
Now, we add the positive terms:
\[ 7x + 5x = 12x \]

### Step 4: Add the negative terms
Next, we add the negative terms:
\[ -3x + (-x) + (-2x) = -3x - x - 2x \]
This simplifies to:
\[ -3x - 1x - 2x = -6x \]

### Step 5: Combine the results
Now we combine the results from the positive and negative terms:
\[ 12x + (-6x) = 12x - 6x = 6x \]

### Final Answer
Thus, the final result of adding the expressions \(7x, -3x, 5x, -x, -2x\) is:
\[ \boxed{6x} \]

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