which equaction has no solution select all that apply
8k+38=-3(-6-4k)
36-7y=-7(y-5)
-2(w-2)=-3-2w
-4(x+3)=-12-4x
The equation that has no solution is:
-2(w-2) = -3-2w
To find the equations that have no solution, we need to analyze each equation separately:
1) 8k + 38 = -3(-6 - 4k)
Expand the brackets:
8k + 38 = 18 + 12k
Rearrange terms:
8k - 12k = 18 - 38
-4k = -20
Divide both sides by -4:
k = 5
This equation does have a solution, so it is not an equation with no solution.
2) 36 - 7y = -7(y - 5)
Expand the brackets:
36 - 7y = -7y + 35
Rearrange terms:
36 - 35 = -7y + 7y
1 = 0
This equation leads to a contradiction (1 = 0), meaning there is no solution. Therefore, this equation has no solution.
3) -2(w - 2) = -3 - 2w
Expand the brackets:
-2w + 4 = -3 - 2w
Combine like terms:
-2w + 2w = -3 - 4
0 = -7
This equation also leads to a contradiction (0 = -7), so it has no solution.
4) -4(x + 3) = -12 - 4x
Expand the brackets:
-4x - 12 = -12 - 4x
Rearrange terms:
-4x + 4x = -12 + 12
0 = 0
This equation is always true (0 = 0), so it has infinitely many solutions. Therefore, it does not have no solution.
In conclusion, the equations with no solution are:
-2(w-2) = -3 - 2w
36-7y = -7(y-5)
To determine which equation has no solution, we need to simplify each equation and see if the variable cancels out, resulting in a false statement that cannot be solved.
1. 8k + 38 = -3(-6 - 4k):
First, distribute -3 to (-6 - 4k): -3 * -6 - 3 * 4k = 18 + 12k.
The equation then becomes: 8k + 38 = 18 + 12k.
Next, let's try to simplify further: Subtract 8k from both sides: 38 = 18 + 4k.
Subtract 18 from both sides: 20 = 4k.
Finally, divide by 4: k = 5.
Since we were able to solve for k, this equation does have a solution.
2. 36 - 7y = -7(y - 5):
First, distribute -7 to (y - 5): -7y + 35.
The equation then becomes: 36 - 7y = -7y + 35.
Next, let's try to simplify further: Add 7y to both sides: 36 = 35.
This is not possible since 36 cannot equal 35.
Therefore, this equation has no solution.
3. -2(w - 2) = -3 - 2w:
First, distribute -2 to (w - 2): -2w + 4.
The equation then becomes: -2w + 4 = -3 - 2w.
Next, let's try to simplify further: Add 2w to both sides: 4 = -3.
This is not possible since 4 cannot equal -3.
Therefore, this equation has no solution.
4. -4(x + 3) = -12 - 4x:
First, distribute -4 to (x + 3): -4x - 12.
The equation then becomes: -4x - 12 = -12 - 4x.
Next, let's try to simplify further: Add 4x to both sides: -12 = -12.
In this case, the variables cancel out, and we are left with a true statement.
Therefore, this equation has infinitely many solutions.
The equations that have no solution are:
2. 36 - 7y = -7(y - 5)
3. -2(w - 2) = -3 - 2w