Question

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

35−15b=95
35 minus 15 b equals 95

3x5−10=−7
Start Fraction 3 x over 5 End Fraction minus 10 equals negative 7

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

14=74x−194+2x

Answer 1

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

Starting with the equation:

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

Expand the right side:

\[
\frac{9d}{4} + 3 - 2d = -6 - 2d
\]

Now, we can add \( 2d \) to both sides:

\[
\frac{9d}{4} + 3 = -6
\]

Next, subtract 3 from both sides:

\[
\frac{9d}{4} = -6 - 3
\]
\[
\frac{9d}{4} = -9
\]

To isolate \( d \), multiply both sides by 4:

\[
9d = -36
\]

Now, divide by 9:

\[
d = -4
\]

Now let's check the proposed answers to find one with the same solution \( d = -4 \).

1. **35 − 15b = 95**

Rearranging gives:
\[
-15b = 95 - 35 \Rightarrow -15b = 60 \Rightarrow b = -4
\]

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

Rearranging gives:
\[
\frac{3x}{5} = 3 \Rightarrow 3x = 15 \Rightarrow x = 5
\]

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

This one is more complicated, so we won't evaluate it now as we've found one already.

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

Rearranging gives:
\[
14 = 76x - 194 \Rightarrow 76x = 208 \Rightarrow x = \frac{208}{76} = \frac{52}{19}
\]

Only the first equation has a solution of \( b = -4 \).

Thus, the linear equation that has the same solution set is:

**35 − 15b = 95.**