Question

Which linear equation has the same solution set as 9d4+3−2d=−2(3+d)?(1 point)Responses4w−2(7−3w)=w3−64 w minus 2 left parenthesis 7 minus 3 w right parenthesis equals Start Fraction w over 3 End Fraction minus 63x5−10=−7Start Fraction 3 x over 5 End Fraction minus 10 equals negative 735−15b=9535 minus 15 b equals 9514=74x−194+2x

Answer 1

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

Starting with the original equation:

\[
9d^4 + 3 - 2d = -2(3 + d)
\]

Expanding the right side:

\[
-2(3 + d) = -6 - 2d
\]

Now, substituting that back into the equation:

\[
9d^4 + 3 - 2d = -6 - 2d
\]

Now, we can cancel \(-2d\) from both sides:

\[
9d^4 + 3 = -6
\]

Next, we can isolate \(9d^4\) by subtracting 3 from both sides:

\[
9d^4 = -6 - 3
\]

\[
9d^4 = -9
\]

Divide by 9:

\[
d^4 = -1
\]

Since we are looking for a linear equation with the same solution set, we know that the equation \(d^4 = -1\) has no real solutions (as there are no real numbers whose fourth power equals -1).

Looking at the given responses, we inspect each equation to identify which has the same solution set (no real solutions):

1. **Option 1:** \(4w - 2(7 - 3w) = \frac{w}{3} - 6\)
2. **Option 2:** \(5 - 10 = -7\)
3. **Option 3:** \(5 - 15b = 95\)
4. **Option 4:** \(14 = 7(4x - 19) + 2x\)

Now let's analyze each option:

1. The first equation can be simplified and should be checked for valid \(w\).
2. The second equation simplifies to \(5 - 10 = -7\), which is not valid (no solution).
3. The third simplifies to a value for \(b\) (valid).
4. The fourth equation can be manipulated; one would expect to either find a solution or no valid solutions.

Since we are looking for no real solutions, we see that the second one, \(5 - 10 = -7\) has no valid solution.

Thus, the answer is:

**5 - 10 = -7** which has the same solution set as \(9d^4 + 3 - 2d = -2(3 + d)\).