Question

Which linear equation has the same solution set
9d/4+3 - 2d = -2 (3+d)?
(1 point)
4w - 2(7 - 3w) = w/3 - 6
14 = 7/4x - 19/4 + 2x
3x/5－10=-7
35 — 15b = 95

Answer 1

To determine which linear equation has the same solution set as the provided equation \( 9d/4 + 3 - 2d = -2(3 + d) \), let's first solve the given equation step by step.

1. **Rewrite the equation:**
\[
\frac{9d}{4} + 3 - 2d = -2(3 + d)
\]

2. **Distributing on the right side:**
\[
-2(3 + d) = -6 - 2d
\]
Thus, the equation becomes:
\[
\frac{9d}{4} + 3 - 2d = -6 - 2d
\]

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

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

5. **Multiplying both sides by \(\frac{4}{9}\):**
\[
d = -4
\]

Now, we have found that the solution to the equation is \( d = -4 \).

Next, we will check which of the provided equations also has \( d = -4 \) as a solution.

**Option 1:**
\[
4w - 2(7 - 3w) = \frac{w}{3} - 6
\]
Distributing on the left:
\[
4w - 14 + 6w = \frac{w}{3} - 6
\]
Combining like terms:
\[
10w - 14 = \frac{w}{3} - 6
\]
Multiplying through by 3 to eliminate the fraction:
\[
30w - 42 = w - 18
\]
Now collect terms:
\[
29w = 24 \quad \therefore \quad w = \frac{24}{29}
\]
**(Not equal to -4)**

**Option 2:**
\[
14 = \frac{7}{4} x - \frac{19}{4} + 2x
\]
Combining terms on the right:
\[
14 = \left( \frac{7}{4} + \frac{8}{4} \right)x - \frac{19}{4}
\]
\[
14 = \frac{15}{4}x - \frac{19}{4}
\]
Multiplying through by 4:
\[
56 = 15x - 19
\]
Adding 19:
\[
75 = 15x \quad \therefore \quad x = 5
\]
**(Not equal to -4)**

**Option 3:**
\[
\frac{3x}{5} - 10 = -7
\]
Adding 10 to both sides:
\[
\frac{3x}{5} = 3
\]
Multiplying both sides by 5:
\[
3x = 15 \quad \therefore \quad x = 5
\]
**(Not equal to -4)**

**Option 4:**
\[
35 - 15b = 95
\]
Subtracting 35 from both sides:
\[
-15b = 60 \quad \therefore \quad b = -4
\]

**Conclusion:**
The equation that has the same solution set as \( 9d/4 + 3 - 2d = -2(3 + d) \) is:
\[
\boxed{35 - 15b = 95}
\] because it has the same solution \( b = -4 \).