Which linear equation has the same solution set as 9d/4+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
The correct linear equation that has the same solution set as 9d/4 + 3 - 2d = -2(3 + d) is 3x/5 - 10 = -7.
To find the linear equation that has the same solution set as 9d/4+3−2d=−2(3+d), we need to simplify the given equation first.
9d/4 + 3 - 2d = -2(3 + d)
Let's start by distributing -2 to (3 + d):
9d/4 + 3 - 2d = -6 - 2d
Next, let's combine like terms on both sides:
9d/4 - 2d = -6 - 2d - 3
To get rid of the fractions, we can multiply everything by 4:
4(9d/4 - 2d) = 4(-6 - 2d - 3)
9d - 8d = -24 - 8d - 12
d = -24 - 8d - 12
Now, let's simplify the equation:
d + 8d = -24 - 12
9d = -36
Lastly, divide both sides by 9 to solve for d:
d = -36/9
d = -4
So, the solution to the given equation is d = -4.
Now, let's check which of the provided options has the same solution set.
1) 4w - 2(7 - 3w) = w/3 - 6
2) 14 = 7/4x - 19/4 + 2x
3) 35 - 15b = 95
4) 3x/5 - 10 = -7
To check if any of these equations have the same solution set, we substitute d = -4 into each equation and see if it holds true.
1) 4w - 2(7 - 3w) = w/3 - 6
Substituting d = -4:
4w - 2(7 - 3w) = w/3 - 6
4w - 14 + 6w = -4/3 - 6
10w - 14 = -4/3 - 18/3
10w - 14 = -22/3
This equation does not hold true, so option 1 is not the correct answer.
2) 14 = 7/4x - 19/4 + 2x
Substituting d = -4:
14 = 7/4x - 19/4 + 2x
Multiplying by 4 to get rid of the fractions:
56 = 7x - 19 + 8x
56 = 15x - 19
15x = 56 + 19
15x = 75
x = 75/15
x = 5
This equation holds true, so option 2 is the correct answer.
Therefore, the linear equation that has the same solution set as 9d/4+3−2d=−2(3+d) is:
14 = 7/4x - 19/4 + 2x.
To determine which linear equation has the same solution set as the given equation, we need to solve the given equation and then compare the solutions to the answer choices. Let's go through the process step by step.
Given equation: 9d/4 + 3 - 2d = -2(3 + d)
1. To begin, simplify the equation by distributing the negative sign on the right side:
9d/4 + 3 - 2d = -6 - 2d
2. Next, combine like terms on both sides of the equation:
(9d/4 - 2d) + 3 = -6 - 2d
Simplifying further:
(9d - 8d)/4 + 3 = -6 - 2d
-d/4 + 3 = -6 - 2d
3. To eliminate the fractions, multiply every term in the equation by 4:
4(-d/4 + 3) = 4(-6 - 2d)
Simplifying further:
-d + 12 = -24 - 8d
4. Now, collect like terms on both sides:
-d + 8d = -24 - 12
Simplifying further:
7d = -36
5. Divide both sides of the equation by 7 to solve for d:
7d/7 = -36/7
Simplifying further:
d = -36/7
Now that we have the solution for d, let's check which answer choice will yield the same solution.
Option 1: 4w - 2(7 - 3w) = w/3 - 6
Option 2: 14 = 7/4x - 19/4 + 2x
Option 3: 35 - 15b = 95
Option 4: 3x/5 - 10 = -7
Substitute d = -36/7 into each equation and see which one gives us a true statement.
For Option 1:
4w - 2(7 - 3w) = w/3 - 6
After simplifying, this equation does not yield d = -36/7.
For Option 2:
14 = 7/4x - 19/4 + 2x
After simplifying, this equation does not yield d = -36/7.
For Option 3:
35 - 15b = 95
After simplifying, this equation does not involve the variable d.
For Option 4:
3x/5 -10 = -7
After simplifying, this equation also does not involve the variable d.
Therefore, none of the provided answer choices has the same solution set as the given equation.