Question
Which linear equation has the same solution set as a + 3 - 2d = -2 (3 + d)? (1 point)
• 4w - 2(7 - 3ш) =
- 6
3
O 14 = 7
X -
4
19 + 2x
2-10=-7
• 35 - 156 = 95
• 4w - 2(7 - 3ш) =
- 6
3
O 14 = 7
X -
4
19 + 2x
2-10=-7
• 35 - 156 = 95
Answers
GPT-4o mini
To determine which linear equation has the same solution set as \( a + 3 - 2d = -2(3 + d) \), we first need to simplify the given equation.
1. Start by distributing on the right side of the equation:
\[
a + 3 - 2d = -2(3 + d) = -6 - 2d
\]
2. Now, rewrite the equation:
\[
a + 3 - 2d = -6 - 2d
\]
3. We can notice that \(-2d\) on both sides cancels out:
\[
a + 3 = -6
\]
4. Now, solve for \(a\):
\[
a = -6 - 3 = -9
\]
Now we have the solution \( a = -9 \).
Next, we should check the options provided to find an equivalent equation that gives the same solution \(a = -9\). However, the options listed seem to have some incorrect characters and formatting issues.
If we replace "w" with "x" in the first equation:
- Suppose it reads as: **4x - 2(7 - 3x) = -6**
Let's simplify it:
\[
4x - 14 + 6x = -6
\]
Combine like terms:
\[
10x - 14 = -6
\]
Add 14:
\[
10x = 8
\]
Divide by 10:
\[
x = \frac{8}{10} = 0.8
\]
Since none of the conditions match up to \(a = -9\), and the rest of the equations have similar ambiguities, it is hard to conclusively relate them to the simplified form unless they are clarified correctly.
To sum up, without clearer options or specific values, it’s challenging to identify a correct linear equation that matches \( a = -9\). Please provide clear equations to compare against.
1. Start by distributing on the right side of the equation:
\[
a + 3 - 2d = -2(3 + d) = -6 - 2d
\]
2. Now, rewrite the equation:
\[
a + 3 - 2d = -6 - 2d
\]
3. We can notice that \(-2d\) on both sides cancels out:
\[
a + 3 = -6
\]
4. Now, solve for \(a\):
\[
a = -6 - 3 = -9
\]
Now we have the solution \( a = -9 \).
Next, we should check the options provided to find an equivalent equation that gives the same solution \(a = -9\). However, the options listed seem to have some incorrect characters and formatting issues.
If we replace "w" with "x" in the first equation:
- Suppose it reads as: **4x - 2(7 - 3x) = -6**
Let's simplify it:
\[
4x - 14 + 6x = -6
\]
Combine like terms:
\[
10x - 14 = -6
\]
Add 14:
\[
10x = 8
\]
Divide by 10:
\[
x = \frac{8}{10} = 0.8
\]
Since none of the conditions match up to \(a = -9\), and the rest of the equations have similar ambiguities, it is hard to conclusively relate them to the simplified form unless they are clarified correctly.
To sum up, without clearer options or specific values, it’s challenging to identify a correct linear equation that matches \( a = -9\). Please provide clear equations to compare against.