Which equation has no solution? Select all that apply. (1 point) Responses 8k+38=−3(−6−4k)8k+38=−3(−6−4k) 8 k plus 38 is equal to negative 3 times open paren negative 6 minus 4 k close paren −2(w−2)=−3−2w−2(w−2)=−3−2w negative 2 times open paren w minus 2 close paren is equal to negative 3 minus 2 w 36−7y=−7(y−5)36−7y=−7(y−5) 36 minus 7 y is equal to negative 7 times open paren y minus 5 close paren −4(x+3)=−12−4x−4(x+3)=−12−4x negative 4 times open paren x plus 3 close paren is equal to negative 12 minus 4 x
The equations that have no solution are:
-2(w-2)=-3-2w
36-7y=-7(y-5)
To determine which equation has no solution, let's solve each equation step-by-step:
1) 8k + 38 = -3(-6 - 4k)
First, distribute -3 to -6 and -4k:
8k + 38 = 18 + 12k
Combine like terms by subtracting 12k from both sides:
8k - 12k + 38 = 18
-4k + 38 = 18
Next, subtract 38 from both sides:
-4k + 38 - 38 = 18 - 38
-4k = -20
Now, divide both sides by -4:
-4k / -4 = -20 / -4
k = 5
So, this equation does have a solution.
2) -2(w - 2) = -3 - 2w
First, distribute -2 to w and 2:
-2w + 4 = -3 - 2w
Next, rearrange the equation by moving all terms with w to one side:
-2w + 2w + 4 = -3 - 2w + 2w
4 = -3
This equation leads to a contradiction (4 does not equal -3), meaning it has no solution.
3) 36 - 7y = -7(y - 5)
First, distribute -7 to y and 5:
36 - 7y = -7y + 35
Next, move all terms with y to one side:
36 - 7y + 7y = -7y + 7y + 35
36 = 35
This equation is also a contradiction (36 does not equal 35), meaning it has no solution.
4) -4(x + 3) = -12 - 4x
First, distribute -4 to x and 3:
-4x - 12 = -12 - 4x
Next, move all terms with x to one side:
-4x + 4x - 12 = -12 + 4x + 4x
-12 = -12
This equation is an identity (both sides are equal), meaning it has infinite solutions.
Therefore, the equations that have no solution are:
-2(w - 2) = -3 - 2w
36 - 7y = -7(y - 5)
To find out which equation(s) have no solution, we need to solve each equation and see if the variable disappears or if there is a contradiction.
1. 8k + 38 = -3(-6-4k):
Let's simplify both sides of the equation:
8k + 38 = 18 + 12k
Now, let's move the variables to one side and the constants to the other side:
8k - 12k = 18 - 38
-4k = -20
Dividing both sides by -4:
k = 5
Since we obtained a specific value for k, this equation has a solution. Therefore, it is not the correct answer.
2. -2(w - 2) = -3 - 2w:
Expanding the brackets:
-2w + 4 = -3 - 2w
Notice that the equation simplifies to 4 = -3, which is not true. Thus, we have a contradiction.
Hence, the equation -2(w - 2) = -3 - 2w has no solution.
3. 36 - 7y = -7(y - 5):
Expanding the brackets:
36 - 7y = -7y + 35
Subtracting -7y from both sides:
36 = 35
Again, we end up with a contradiction where 36 is not equal to 35. Therefore, this equation has no solution.
4. -4(x + 3) = -12 - 4x:
Expanding the brackets:
-4x - 12 = -12 - 4x
Notice that the equation simplifies to -12 = -12, which is always true. Therefore, all values of x satisfy this equation, meaning it has infinitely many solutions.
In conclusion:
The equations that have no solution are: -2(w - 2) = -3 - 2w and 36 - 7y = -7(y - 5).