Question

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

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

14=74x−19/4+2x
14 equals Start Fraction 7 over 4 End Fraction x minus Start Fraction 19 over 4 End Fraction plus 2 x

35−15b=95
35 minus 15 b equals 95

4w−2(7−3w)=w/3−6

Answer 1

To find which linear equation has the same solution set as \( \frac{9}{d} + 3 - 2d = -2(3 + d) \), we will first simplify the given equation step by step:

1. Start with the original equation:
\[
\frac{9}{d} + 3 - 2d = -2(3 + d)
\]

2. Distribute on the right side:
\[
-2(3 + d) = -6 - 2d
\]
So the equation becomes:
\[
\frac{9}{d} + 3 - 2d = -6 - 2d
\]

3. Next, add \(2d\) to both sides:
\[
\frac{9}{d} + 3 = -6
\]

4. Subtract 3 from both sides:
\[
\frac{9}{d} = -9
\]

5. Multiply both sides by \(d\) (assuming \(d \neq 0\)):
\[
9 = -9d
\]

6. Finally, divide both sides by -9 to solve for \(d\):
\[
d = -1
\]

Now we know that the original equation has the solution \(d = -1\). We need to check which of the given equations have the same solution.

Let's check each response:

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

Solving this:
\[
\frac{3x}{5} = 3
\]
\[
3x = 15
\]
\[
x = 5
\]

2. **Response:** \( 14 = \frac{7}{4} x - \frac{19}{4} + 2x \)

Rearranging to solve for \(x\):
\[
14 + \frac{19}{4} = \frac{7}{4}x + 2x
\]
Convert \(14\) to quarters:
\[
\frac{56}{4} + \frac{19}{4} = \frac{7}{4}x + \frac{8}{4}x
\]
\[
\frac{75}{4} = \frac{15}{4}x
\]
\[
x = 5
\]

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

Solving this:
\[
-15b = 95 - 35
\]
\[
-15b = 60
\]
\[
b = -4
\]

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

Simplifying:
\[
4w - 14 + 6w = \frac{w}{3} - 6
\]
\[
10w - 14 = \frac{w}{3} - 6
\]
Multiply the entire equation by \(3\) to eliminate the fraction:
\[
30w - 42 = w - 18
\]
\[
29w = 24
\]
\[
w = \frac{24}{29}
\]

None of these equations give the solution \(d = -1\), but there seems to have been a misunderstanding about how to analyze which equation corresponds to \(d = -1\).

Thus, **none of the offered responses yield a solution of -1.** Please verify if you meant for any specific numerical form or change in sign, or if the terms were supposed to remain abstract and unaltered from the starting.