Which linear equation has the same solution set as 9d4+3−2d=−2(3+d) ? Responses 35−15b=95 35 minus 15 b equals 95 3x5−10=−7 Start Fraction 3 x over 5 End Fraction minus 10 equals negative 7 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 14=74x−194+2x
The linear equation that has the same solution set as 9d4+3−2d=−2(3+d) is 35−15b=95.
To determine which linear equation has the same solution set as 9d4+3−2d=−2(3+d), we need to simplify the given equation and then compare it with the options provided.
Let's solve the given equation step by step:
9d4 + 3 − 2d = −2(3 + d)
Expanding the right side of the equation:
9d4 + 3 − 2d = -6 - 2d
Moving the variable terms to one side:
9d4 + 2d + 2d = -6 - 3
Combining like terms:
9d4 + 4d = -9
Comparing this equation with the options provided:
a) 35−15b=95
b) 3x5−10=−7
c) 4w−2(7−3w)=w3−6
d) 14=74x−194+2x
None of the options matches the simplified equation we obtained. Therefore, none of the given options has the same solution set as the original equation.
To find the linear equation that has the same solution set as the given equation, we need to simplify the given equation and rewrite it in the standard linear form of "y = mx + b", where "m" represents the slope and "b" represents the y-intercept.
Let's simplify the given equation: 9d4 + 3 - 2d = -2(3 + d)
Start by distributing the -2 on the right side of the equation: -2 * 3 - 2 * d = -6 - 2d
Now, simplify further by combining like terms: -6 - 2d = -6 - 2d
We can see that both sides of the equation are equal, so any value of "d" would satisfy this equation. This implies that any equation with "d" as the variable will have the same solution set.
Therefore, any of the provided linear equations (35 - 15b = 95, (3x5/5) - 10 = -7, 4w - 2(7 - 3w) = (w/3) - 6, 14 = 74x - 19(4 + 2x)) could have the same solution set as the given equation.