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

Question

Responses

14=74x−194+2x
14 equals Start Fraction 7 over 4 End Fraction x minus Start Fraction 19 over 4 End Fraction plus 2 x

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

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

35−15b=95

Answer 1

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

Starting with the original equation:

1. Distribute the right-hand side: \[ \frac{9d}{4} + 3 - 2d = -6 - 2d \]

2. Add \(2d\) to both sides: \[ \frac{9d}{4} + 3 = -6 \]

3. Move \(3\) to the right-hand side: \[ \frac{9d}{4} = -9 \]

4. Multiply both sides by \(4\): \[ 9d = -36 \]

5. Divide by \(9\): \[ d = -4 \]

Now we have determined the solution \(d = -4\). Let's analyze the choices given and see which one simplifies to the same solution:

1. Option 1: \[ 14 = \frac{7}{4}x - \frac{19}{4} + 2x \] This needs to be investigated further.

2. Option 2: \[ 4w - 2(7 - 3w) = \frac{w}{3} - 6 \] This also requires investigation.

3. Option 3: \[ \frac{3x}{5} - 10 = -7 \] Let's try solving this one:

   • Add \(10\) to both sides: \[ \frac{3x}{5} = 3 \]
   • Multiply by \(5\): \[ 3x = 15 \]
   • Divide by \(3\): \[ x = 5 \] This does not match.

4. Option 4: \[ 35 - 15b = 95 \] Solving:

   • Subtract \(35\): \[ -15b = 60 \]
   • Dividing by \(-15\): \[ b = -4 \] This matches our solution.

Thus, the linear equation that has the same solution set as \( \frac{9d}{4} + 3 - 2d = -2(3 + d) \) is: \[ \boxed{35 - 15b = 95} \]