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Reduce the expression:



\[ 2w - 17c + [-4x + 9y] - [-5w + 14x - 8c] \]



Solve:



1. Eliminate the grouping symbols:



\[ 2w - 17c - 4x + 9y + 5w - 14x + 8c \]



2. Combine like terms:



\[ (2w + 5w) + (-17c + 8c) + (-4x - 14x) + 9y \]



\[ 7w - 9c - 18x + 9y \]

Answer :

We start with the expression

$$
2w - 17c + \big[-4x + 9y\big] - \big[-5w + 14x - 8c\big].
$$

**Step 1. Remove the Collection Signs**

Since the brackets do not affect the terms in the first bracket, we have:

$$
2w - 17c -4x + 9y.
$$

For the second bracket, notice that there is a minus sign in front. Distribute the minus sign (i.e., multiply each term by \(-1\)):

$$
- \big(-5w + 14x - 8c\big) = 5w - 14x + 8c.
$$

So, the whole expression becomes:

$$
2w - 17c - 4x + 9y + 5w - 14x + 8c.
$$

**Step 2. Combine Like Terms**

Now, group like terms by variable:

- For \(w\):

$$
2w + 5w = 7w.
$$

- For \(c\):

$$
-17c + 8c = -9c.
$$

- For \(x\):

$$
-4x - 14x = -18x.
$$

- For \(y\):

$$
9y \quad (\text{this term stands alone}).
$$

**Step 3. Write the Final Answer**

Putting it all together, the reduced expression is:

$$
7w - 9c - 18x + 9y.
$$

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Rewritten by : Barada