Question

Select the expressions that are equivalent to – 2(7a–1)–3a.
1) -2(-9a+16a-1)-3a
2)-2(-1+7a)-3a
3) -2(3a+4a-1)-3a
4)-17a+2

Answer 1

To determine which expressions are equivalent to \(-2(7a-1)-3a\), we will simplify the original expression and then each of the options.

1. **Original expression:**
\[
-2(7a - 1) - 3a = -2 \cdot 7a + 2 \cdot 1 - 3a = -14a + 2 - 3a = -14a - 3a + 2 = -17a + 2
\]

Now let's simplify each of the options:

1) \(-2(-9a + 16a - 1) - 3a\):
\[
-2(-9a + 16a - 1) = -2(7a - 1) = -2 \cdot 7a + 2 \cdot 1 = -14a + 2
\]
Then subtracting \(3a\):
\[
-14a + 2 - 3a = -14a - 3a + 2 = -17a + 2
\]

2) \(-2(-1 + 7a) - 3a\):
\[
-2(-1 + 7a) = -2 \cdot (-1) + -2 \cdot (7a) = 2 - 14a
\]
Then subtracting \(3a\):
\[
2 - 14a - 3a = 2 - 17a
\]

3) \(-2(3a + 4a - 1) - 3a\):
\[
-2(3a + 4a - 1) = -2(7a - 1) = -14a + 2
\]
Then subtracting \(3a\):
\[
-14a + 2 - 3a = -14a - 3a + 2 = -17a + 2
\]

4) \(-17a + 2\):
This expression is already in the form we derived earlier.

Now, let's compare the results:

- **Option 1**: \(-17a + 2\) (equivalent to original)
- **Option 2**: \(2 - 17a\) (not equivalent)
- **Option 3**: \(-17a + 2\) (equivalent to original)
- **Option 4**: \(-17a + 2\) (equivalent to original)

Thus, the equivalent expressions are:
**1, 3, and 4**.