Which expressions are equivalent to -9 (2/3x + 1) Check the two that apply.

Question

(2 points)
• -6x - 9
-9 (2/3x) - 9(1)
* -6x + 9
* -9 (2/3x) + 9 (1)
* -6x + 1

Answer 1

To determine which expressions are equivalent to $-9(\frac{2}{3}x+1)$, we'll first simplify this expression.

1. Distribute $-9$:

$$-9(\frac{2}{3}x+1)=-9\cdot \frac{2}{3}x-9\cdot 1$$

2. Calculate $-9\cdot \frac{2}{3}x$:

$$-9\cdot \frac{2}{3}=-6$$ So this part becomes $-6x$.

3. Now subtract $9$:

$$-6x-9$$

Thus, the original expression simplifies to:

$$-6x-9$$

Now let's compare this with each of the given options to find which ones are equivalent to $-9(\frac{2}{3}x+1)$:

1. -6x - 9 (This is equivalent, as shown.)
2. -9 (2/3x) - 9(1) (This is equivalent as it expands to $-6x-9$.)
3. -6x + 9 (Not equivalent, since this would equal $-6x$ plus a positive $9$.)
4. -9 (2/3x) + 9 (1) (This simplifies to $-6x+9$, not equivalent.)
5. -6x + 1 (Not equivalent, as it does not match.)

So, the two expressions that are equivalent to $-9(\frac{2}{3}x+1)$ are:

• $-6x-9$
• $-9(2/3x)-9(1)$

Therefore the correct selections are:

• -6x - 9
• -9 (2/3x) - 9(1)