Which linear equation has the same solution set as 9d4+3−2d=−2(3+d) ?(1 point) Responses
4w−2(7−3w)=w/3−6
14=7/4x−19/4+2x
35−15b=95
3x/5−10=−7
To find the linear equation that has the same solution set as 9d4+3−2d=−2(3+d), we need to simplify the given equation first.
9d4+3−2d=−2(3+d)
Simplifying the equation, we get:
9d^4 + 3 - 2d = -6 - 2d
Next, we can combine like terms:
9d^4 + 3 = -6
To isolate the variable term, we subtract 3 from both sides:
9d^4 = -9
Finally, we divide both sides by 9 to solve for d:
d^4 = -1
The equation d^4 = -1 represents an equation with complex solutions, which cannot be directly translated into a linear equation. Therefore, none of the provided options (4w−2(7−3w)=w/3−6, 14=7/4x−19/4+2x, 35−15b=95, 3x/5−10=−7) have the same solution set as the original equation.
To find a linear equation with the same solution set as the given equation 9d4 + 3 - 2d = -2(3 + d), we need to simplify the given equation and manipulate it to match the form of a linear equation, which is in the form of y = mx + b.
Let's solve the given equation step by step:
9d4 + 3 - 2d = -2(3 + d)
Firstly, distribute -2 on the right side:
9d4 + 3 - 2d = -6 - 2d
Next, combine like terms on both sides:
9d4 + 3 = -6
Now, subtract 3 from both sides to isolate the variable:
9d4 = -9
Lastly, divide both sides by 9 to solve for d:
d4 = -1
Now, to create a linear equation with the same solution set, we can assume any constant value for d. Let's assume d = 1.
Substituting d = 1 in the original equation:
9(1)4 + 3 - 2(1) = -2(3 + 1)
9 + 3 - 2 = -2(4)
10 = -8
Since 10 is not equal to -8, d = 1 is not a valid solution.
Therefore, no linear equation will have the same solution set as the given equation 9d4 + 3 - 2d = -2(3 + d).