ब) Write an expression that is equivalent to $$ 9 c-12-15 c-8-3 c $$. (1)) Which sum is equivalent to $$ 9 c-12-15 c-8-3 c $$ ? \begin{tabular}{|c|}\hline $$ 9 c+12+15 c+8+3 c $$ \ \hline$$ -9 c+(-12)+(-15 c)+(-8)+(-3 c) $$ \ $$ 9 c+(-12)+(-15 c)+(-8)+(-3 c) $$ \ \hline $$ 9 c+(-12)-15 c+(-8)-3 c $$ \ \hline\end{tabular}

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UpStudy AI · Accepted Answer

To solve the expression $$ 9c - 12 - 15c - 8 - 3c $$, we will first combine like terms step by step.

1. **Identify like terms**: 
   - The terms involving $$ c $$ are $$ 9c $$, $$ -15c $$, and $$ -3c $$.
   - The constant terms are $$ -12 $$ and $$ -8 $$.

2. **Combine the $$ c $$ terms**:
   $$
   9c - 15c - 3c = (9 - 15 - 3)c = -9c
   $$

3. **Combine the constant terms**:
   $$
   -12 - 8 = -20
   $$

4. **Combine the results**:
   $$
   -9c - 20
   $$

Now, we have simplified the expression to $$ -9c - 20 $$.

Next, we need to determine which sum is equivalent to $$ 9c - 12 - 15c - 8 - 3c $$ from the provided options.

Let's analyze the options:

1. $$ 9c + 12 + 15c + 8 + 3c $$ - This is not equivalent because it adds instead of subtracting.
2. $$ -9c + (-12) + (-15c) + (-8) + (-3c) $$ - This is not equivalent because it changes the signs incorrectly.
3. $$ 9c + (-12) + (-15c) + (-8) + (-3c) $$ - This is not equivalent because it does not correctly represent the original expression.
4. $$ 9c + (-12) - 15c + (-8) - 3c $$ - This is equivalent to the original expression because it maintains the correct signs.

Thus, the correct answer is:

**The equivalent expression is $$ -9c - 20 $$**, and the sum that is equivalent to $$ 9c - 12 - 15c - 8 - 3c $$ is:

**Option 4: $$ 9c + (-12) - 15c + (-8) - 3c $$**.
The equivalent expression is $$ -9c - 20 $$.

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