which equation has no solution? select all that apply
-4(x+3)=12-4x
-2(w-2)=-3-2w
8k+38=-3(-6-4k)
36-7y=-7(y-5)
-4(x+3)=12-4x
To determine which equations have no solution, we need to simplify each equation and check if the variables cancel out or result in a contradiction. Let's analyze each equation one by one:
1. -4(x + 3) = 12 - 4x:
Expanding the brackets yields -4x - 12 = 12 - 4x. Rearranging this equation gives -4x + 4x = 12 + 12, which simplifies to 0 = 24. Since this is not true, there is no solution for this equation.
2. -2(w - 2) = -3 - 2w:
Expanding the brackets gives -2w + 4 = -3 - 2w. Rearranging this equation results in -2w + 2w = -3 - 4, which simplifies to 0 = -7. Since this is not true, there is no solution for this equation.
3. 8k + 38 = -3(-6 - 4k):
Simplifying the right side of the equation first gives -3(-6 - 4k) = 18 + 12k. Now, our equation becomes 8k + 38 = 18 + 12k. By rearranging, we have 8k - 12k = 18 - 38, which simplifies to -4k = -20. Dividing both sides by -4, we get k = 5. Thus, this equation has a solution, k = 5.
4. 36 - 7y = -7(y - 5):
Expanding the brackets yields 36 - 7y = -7y + 35. By rearranging the equation, we have -7y + 7y = 35 - 36, which simplifies to 0 = -1. Since this is not true, there is no solution for this equation.
Therefore, the equations that have no solution are:
-4(x + 3) = 12 - 4x
-2(w - 2) = -3 - 2w
36 - 7y = -7(y - 5)
To determine which equation has no solution, we need to solve each equation and check if it leads to a contradiction or an inconsistency. Let's go through each equation:
1. -4(x+3) = 12-4x
To solve this equation, we can start by distributing the -4 on the left side:
-4x - 12 = 12 - 4x
Now, let's simplify by adding 4x to both sides:
-12 = 12
Since -12 does not equal 12, this equation leads to a contradiction. Therefore, the equation -4(x+3) = 12-4x has no solution.
2. -2(w-2) = -3 - 2w
We can solve this equation in a similar manner by distributing the -2 on the left side:
-2w + 4 = -3 - 2w
Simplifying further, we add 2w to both sides:
4 = -3
Once again, we encounter a contradiction where 4 does not equal -3. Therefore, the equation -2(w-2) = -3 - 2w also has no solution.
3. 8k+38 = -3(-6-4k)
We will rewrite the right side of the equation by multiplying and distributing:
8k+38 = 18 + 12k
Next, we'll simplify by subtracting 12k from both sides:
-4k + 38 = 18
Now, let's subtract 38 from both sides to isolate -4k:
-4k = -20
Finally, we'll divide both sides by -4 to solve for k:
k = 5
In this case, we were able to find a value for k that satisfies the equation. Thus, the equation 8k+38 = -3(-6-4k) has a solution.
4. 36 - 7y = -7(y-5)
To solve this equation, we'll distribute -7 on the right side:
36 - 7y = -7y + 35
Following this, we can simplify by adding 7y to both sides:
36 = 35
Once again, we encounter a contradiction where 36 does not equal 35. Therefore, the equation 36 - 7y = -7(y-5) has no solution.
So, the equations that have no solution are -4(x+3) = 12-4x and 36 - 7y = -7(y-5).