Question

Which linear equation has the same solution set as 9d/4+3−2d=−2(3+d) ?(1 point)
Responses

14=74x−194+2x
14 equals Start Fraction 7 over 4 End Fraction x minus Start Fraction 19 over 4 End Fraction plus 2 x

4w−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=−7
Start Fraction 3 x over 5 End Fraction minus 10 equals negative 7

35−15b=95

Answer 1

To find a linear equation that has the same solution set as \( \frac{9d}{4} + 3 - 2d = -2(3 + d) \), we need to first simplify this equation.

Starting with the original equation:

1. Distribute the right-hand side:
\[
\frac{9d}{4} + 3 - 2d = -6 - 2d
\]

2. Add \(2d\) to both sides:
\[
\frac{9d}{4} + 3 = -6
\]

3. Move \(3\) to the right-hand side:
\[
\frac{9d}{4} = -9
\]

4. Multiply both sides by \(4\):
\[
9d = -36
\]

5. Divide by \(9\):
\[
d = -4
\]

Now we have determined the solution \(d = -4\). Let's analyze the choices given and see which one simplifies to the same solution:

1. **Option 1**:
\[
14 = \frac{7}{4}x - \frac{19}{4} + 2x
\]
This needs to be investigated further.

2. **Option 2**:
\[
4w - 2(7 - 3w) = \frac{w}{3} - 6
\]
This also requires investigation.

3. **Option 3**:
\[
\frac{3x}{5} - 10 = -7
\]
Let's try solving this one:
- Add \(10\) to both sides:
\[
\frac{3x}{5} = 3
\]
- Multiply by \(5\):
\[
3x = 15
\]
- Divide by \(3\):
\[
x = 5
\]
This does not match.

4. **Option 4**:
\[
35 - 15b = 95
\]
Solving:
- Subtract \(35\):
\[
-15b = 60
\]
- Dividing by \(-15\):
\[
b = -4
\]
This matches our solution.

Thus, the linear equation that has the same solution set as \( \frac{9d}{4} + 3 - 2d = -2(3 + d) \) is:
\[
\boxed{35 - 15b = 95}
\]