Question

Which linear equation has the same solution set as 9d4+3−2d=−2(3+d)9d4+3−2d=−2(3+d)?(1 point)

Responses

35−15b=9535−15b=95

35 minus 15 b equals 95

4w−2(7−3w)=w3−64w−2(7−3w)=w3−6

4 w minus 2 left parenthesis 7 minus 3 w right parenthesis equals Start Fraction w over 3 End Fraction minus 6

3x5−10=−73x5−10=−7

Start Fraction 3 x over 5 End Fraction minus 10 equals negative 7

14=74x−194+2x

Answer 1

To determine which linear equation has the same solution set as the given equation \(9d + 3 - 2d = -2(3 + d)\), we will first simplify the given equation.

Starting with the equation:

\[
9d + 3 - 2d = -2(3 + d)
\]

First, simplify the left-hand side:

\[
(9d - 2d) + 3 = 7d + 3
\]

Now simplify the right-hand side:

\[
-2(3 + d) = -6 - 2d
\]

Now we rewrite the equation:

\[
7d + 3 = -6 - 2d
\]

Next, isolate \(d\) by moving all \(d\) terms to one side and constant terms to the other:

\[
7d + 2d = -6 - 3
\]
\[
9d = -9
\]
\[
d = -1
\]

So the solution to the original equation is \(d = -1\).

Now we need to check which of the provided equations also has \(d = -1\) as a solution:

1. **Response 1:** \(35 - 15b = 95\)

This can be simplified:
\[
-15b = 95 - 35 \Rightarrow -15b = 60 \Rightarrow b = -4
\]
This does not have \(d = -1\) as a solution.

2. **Response 2:** \(4w - 2(7 - 3w) = \frac{w}{3} - 6\)

Simplify the left-hand side:
\[
4w - 14 + 6w = 10w - 14
\]
The right-hand side becomes:
\[
\frac{w}{3} - 6
\]
This doesn't lead to an easy isolation of a variable; let's check it later if needed.

3. **Response 3:** \(\frac{3x}{5} - 10 = -7\)

This can be simplified:
\[
\frac{3x}{5} = -7 + 10 \Rightarrow \frac{3x}{5} = 3
\]
\[
3x = 15 \Rightarrow x = 5
\]
The solution here is \(x = 5\) which doesn't match.

4. **Response 4:** \(14 = 74x - 194 + 2x\)

Rearranging gives:
\[
14 = 76x - 194
\]
\[
76x = 14 + 194 \Rightarrow 76x = 208 \Rightarrow x = \frac{208}{76} = \frac{52}{19}
\]
This does not match.

After checking all equations, it seems we must analyze the second one carefully to ensure it provides a solution of \(d = -1\).

Revisiting:

**Response 2:** \(4w - 2(7 - 3w) = \frac{w}{3} - 6\)

Expanding the left-hand side gives:
\[
4w - 14 + 6w = 10w - 14
\]
Set it equal to \(\frac{w}{3} - 6\). Multiply every term by 3 to clear the fraction:
\[
30w - 42 = w - 18
\]
Now, bringing the \(w\) terms together yields:
\[
30w - w = 42 - 18
\]
\[
29w = 24 \Rightarrow w = \frac{24}{29}
\]
Not the correct solution.

**Iteratively correcting away** other calculations — None match the solution sets.

In conclusion, the direct verification upon numeric adjustments shows none of the obtained equations equate to \(d = -1\) originally except clearly observing \glossary into further contextual identities shall map into solving better without blind requests.

None of the equations in the provided responses have the same solution set.