which equaction has no solution select all that apply
8k+38=-3(-6-4k)
36-7y=-7(y-5)
-4(x+3)=-12-4x
The equation -4(x+3)=-12-4x has no solution.
which equaction has no solution select all that apply
8k+38=-3(-6-4k)
36-7y=-7(y-5)
Both equations have a solution.
To determine which equation has no solution, we can solve each equation and verify.
1) 8k + 38 = -3(-6 - 4k)
Let's simplify the equation step-by-step:
8k + 38 = -3(-6 - 4k)
8k + 38 = 18 + 12k // Applying the distributive property
38 - 18 = 12k - 8k
20 = 4k
Now let's solve for k:
20 = 4k
Divide both sides by 4:
20/4 = 4k/4
5 = k
Since we found a value for k (k = 5), this equation has a solution.
2) 36 - 7y = -7(y - 5)
Expanding the equation using the distributive property:
36 - 7y = -7y + 35 // Distribute -7
Now, let's simplify the equation:
36 - 7y = -7y + 35
36 - 35 = -7y + 7y
1 = 0
Here we have obtained a contradiction, 1 = 0, which means there is no solution for this equation.
3) -4(x + 3) = -12 - 4x
Expanding the equation using the distributive property:
-4x - 12 = -12 - 4x
By subtracting -4x from both sides and combining like terms:
-12 = -12
In this case, the equation simplifies to -12 = -12. This is a true statement, indicating that there are infinite solutions to this equation.
In conclusion, the equation that has no solution is: 36 - 7y = -7(y - 5).
To determine which equation has no solution, we need to solve each equation and see if any of them result in an inconsistent statement, such as 1 = 0.
1) For the equation 8k + 38 = -3(-6 - 4k):
First, distribute -3 to the terms inside the parentheses: -3(-6) = 18 and -3(-4k) = 12k.
Then, simplify the equation: 8k + 38 = 18 + 12k.
Combine like terms: 8k - 12k = 18 - 38.
Simplify further: -4k = -20.
Divide both sides of the equation by -4: k = 5.
Since we were able to find a value for k that satisfies the equation, this equation has a solution.
2) For the equation 36 - 7y = -7(y - 5):
Start by distributing -7 to the terms inside the parentheses: -7(y) + 7(5) = -7y + 35.
Simplify the equation: 36 - 7y = -7y + 35.
Move all the y terms to one side of the equation by adding 7y to both sides: 36 = 35.
This equation results in an inconsistent statement, 36 = 35, which means there is no value that can satisfy the equation. Therefore, this equation has no solution.
3) For the equation -4(x + 3) = -12 - 4x:
Start by distributing -4 to the terms inside the parentheses: -4(x) + -4(3) = -4x - 12.
Simplify the equation: -4x - 12 = -12 - 4x.
Notice that both sides of the equation are the same: -4x - 12 = -4x - 12.
This equation is true for all real numbers, which means there are infinite solutions. Therefore, this equation does not have no solution.
Therefore, the equation that has no solution is 36 - 7y = -7(y - 5).