Question

which linear equation has the same solution set as 9d/4 + 3 - 2d= -2(3+d)
A) 35-15b =95
B) 14=7/4 x- 19/4 +2x
C) 4w-2(7-3w)=w/3 - 6
D) 3x/5-10=-7

Answer 1

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

Starting from:
\[
\frac{9d}{4} + 3 - 2d = -2(3 + d)
\]

We can distribute on the right-hand side:
\[
\frac{9d}{4} + 3 - 2d = -6 - 2d
\]

Now, notice that on both sides we have \(-2d\), so we can eliminate \(-2d\) from both sides:
\[
\frac{9d}{4} + 3 = -6
\]

Next, we subtract 3 from both sides:
\[
\frac{9d}{4} = -6 - 3
\]
\[
\frac{9d}{4} = -9
\]

Now, we will multiply both sides by 4 to eliminate the fraction:
\[
9d = -36
\]

Finally, we divide by 9 to solve for \(d\):
\[
d = -4
\]

Now that we have determined that the original equation has a solution of \(d = -4\), we need to check which of the choices also equals \(d = -4\).

### Checking Each Option:

**A)** \( 35 - 15b = 95 \)
\[
-15b = 95 - 35
\]
\[
-15b = 60
\]
\[
b = -4
\]

This implies that \(b = -4\).

**B)** \( 14 = \frac{7}{4} x - \frac{19}{4} + 2x \)
\[
14 = \frac{7}{4} x - \frac{19}{4} + \frac{8}{4} x
\]
\[
14 = \left( \frac{7}{4} + \frac{8}{4} \right)x - \frac{19}{4}
\]
\[
14 = \frac{15}{4} x - \frac{19}{4}
\]
Multiply everything by 4:
\[
56 = 15x - 19
\]
\[
15x = 56 + 19
\]
\[
15x = 75 \implies x = 5
\]

This means \(x \neq -4\).

**C)** \( 4w - 2(7 - 3w) = \frac{w}{3} - 6 \)
\[
4w - 14 + 6w = \frac{w}{3} - 6
\]
\[
10w - 14 = \frac{w}{3} - 6
\]
Multiply everything by 3 to eliminate fractions:
\[
30w - 42 = w - 18
\]
\[
29w = 24 \implies w = \frac{24}{29}
\]

This means \(w \neq -4\).

**D)** \( \frac{3x}{5} - 10 = -7 \)
\[
\frac{3x}{5} = 3
\]
\[
3x = 15 \implies x = 5
\]
This means \(x \neq -4\).

### Conclusion:
The only equation from the options that has the same solution of \(-4\) corresponds to \(b = -4\) in option A.

Thus, the correct answer is **A) \(35 - 15b = 95\)**.