Question

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

Answer 1

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

1. Start by distributing on the right side:
\[
-2(3 + d) = -6 - 2d
\]

2. Rewrite the original equation:
\[
\frac{9d}{4} + 3 - 2d = -6 - 2d
\]

3. To eliminate \( -2d \) from both sides, we can add \( 2d \) to both sides:
\[
\frac{9d}{4} + 3 = -6
\]

4. Next, isolate the term involving \( d \) by subtracting \( 3 \) from both sides:
\[
\frac{9d}{4} = -6 - 3
\]
\[
\frac{9d}{4} = -9
\]

5. Now, eliminate the fraction by multiplying both sides by \( 4 \):
\[
9d = -36
\]

6. Finally, solve for \( d \) by dividing both sides by \( 9 \):
\[
d = -4
\]

Now we have simplified the equation to find that \( d = -4 \). The equivalent linear equation that has the same solution can be obtained from the final step before solving for \( d \):

The simplified equation is:
\[
9d + 36 = 0
\]

Thus, the linear equation that has the same solution set as the original is:
\[
9d + 36 = 0
\]