Which linear equation has the same solution set as 9d4+3−2d=−2(3+d)9d4+3−2d=−2(3+d)?(1 point)

Responses

35−15b=9535−15b=95

35 minus 15 b equals 95

4w−2(7−3w)=w3−64w−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

3x5−10=−73x5−10=−7

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

14=74x−194+2x

1 answer

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

Starting with the equation:

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

First, simplify the left-hand side:

\[ (9d - 2d) + 3 = 7d + 3 \]

Now simplify the right-hand side:

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

Now we rewrite the equation:

\[ 7d + 3 = -6 - 2d \]

Next, isolate \(d\) by moving all \(d\) terms to one side and constant terms to the other:

\[ 7d + 2d = -6 - 3 \] \[ 9d = -9 \] \[ d = -1 \]

So the solution to the original equation is \(d = -1\).

Now we need to check which of the provided equations also has \(d = -1\) as a solution:

  1. Response 1: \(35 - 15b = 95\)

    This can be simplified: \[ -15b = 95 - 35 \Rightarrow -15b = 60 \Rightarrow b = -4 \] This does not have \(d = -1\) as a solution.

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

    Simplify the left-hand side: \[ 4w - 14 + 6w = 10w - 14 \] The right-hand side becomes: \[ \frac{w}{3} - 6 \] This doesn't lead to an easy isolation of a variable; let's check it later if needed.

  3. Response 3: \(\frac{3x}{5} - 10 = -7\)

    This can be simplified: \[ \frac{3x}{5} = -7 + 10 \Rightarrow \frac{3x}{5} = 3 \] \[ 3x = 15 \Rightarrow x = 5 \] The solution here is \(x = 5\) which doesn't match.

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

    Rearranging gives: \[ 14 = 76x - 194 \] \[ 76x = 14 + 194 \Rightarrow 76x = 208 \Rightarrow x = \frac{208}{76} = \frac{52}{19} \] This does not match.

After checking all equations, it seems we must analyze the second one carefully to ensure it provides a solution of \(d = -1\).

Revisiting:

Response 2: \(4w - 2(7 - 3w) = \frac{w}{3} - 6\)

Expanding the left-hand side gives: \[ 4w - 14 + 6w = 10w - 14 \] Set it equal to \(\frac{w}{3} - 6\). Multiply every term by 3 to clear the fraction: \[ 30w - 42 = w - 18 \] Now, bringing the \(w\) terms together yields: \[ 30w - w = 42 - 18 \] \[ 29w = 24 \Rightarrow w = \frac{24}{29} \] Not the correct solution.

Iteratively correcting away other calculations — None match the solution sets.

In conclusion, the direct verification upon numeric adjustments shows none of the obtained equations equate to \(d = -1\) originally except clearly observing \glossary into further contextual identities shall map into solving better without blind requests.

None of the equations in the provided responses have the same solution set.