Select the expressions that are equivalent to $$ -3(-6 x-1)-6 $$. $$ \begin{array}{r}18 x-3 \ (-6 x-1) \cdot-3-6 \ -3(-8 x+2 x-1)-6 \ -6 x-3\end{array} $$ Submit

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The original expression is:

$$
-3(-6x - 1) - 6
$$

Let's simplify it step by step:

1. **Distribute the -3:**
   $$
   -3 \times (-6x) + (-3) \times (-1) = 18x + 3
   $$
   
2. **Subtract 6:**
   $$
   18x + 3 - 6 = 18x - 3
   $$

So, the simplified form of the original expression is $$ 18x - 3 $$.

Now, let's evaluate each of the given options to see which ones are equivalent to the original expression:

1. **$$ 18x - 3 $$**
   - This is exactly the simplified form of the original expression.
   
2. **$$(-6x - 1) \cdot (-3) - 6$$**
   - This is identical to the original expression, just written in a slightly different form.
   
3. **$$-3(-8x + 2x - 1) - 6$$**
   - Simplify inside the parentheses:
     $$
     -8x + 2x = -6x
     $$
     So, the expression becomes:
     $$
     -3(-6x - 1) - 6
     $$
     Which is the original expression.
   
4. **$$-6x - 3$$**
   - This is **not** equivalent to the original expression since the coefficient of $$x$$ differs.

**Therefore, the expressions equivalent to $$ -3(-6x -1) -6 $$ are:**

$$
\begin{array}{r}
18x - 3 \
(-6x - 1) \cdot (-3) - 6 \
-3(-8x + 2x - 1) - 6
\end{array}
$$

**Answer:** All except −6 x − 3 are equivalent to −3(−6x−1)−6.
The expressions equivalent to $$ -3(-6x -1) -6 $$ are: - $$ 18x - 3 $$ - $$ (-6x - 1) \cdot (-3) - 6 $$ - $$ -3(-8x + 2x - 1) - 6 $$ These are all equivalent to the original expression.

Select the expressions that are equivalent to \( -3(-6 x-1)-6 \). \[ \begin{array}{r}18 x-3 \\ (-6 x-1) \cdot-3-6 \\ -3(-8 x+2 x-1)-6 \\ -6 x-3\end{array} \] Submit

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