Which equation has no solution?
(1 point)
Responses
5v + 3 = 5v – 5
5 v + 3 = 5 v – 5
2x – 4 = 2x + 7 – x
2 x – 4 = 2 x + 7 – x
2y + 5 – y = 2y – 3(y – 6)
2 y + 5 – y = 2 y – 3( y – 6)
7z + 9 = –7z – 6
7z + 9 = -7z - 6
To determine which equation has no solution, we need to solve each equation and check if the solution is valid or not. If after solving the equation we arrive at a false statement, such as 2 = 4 or 3 = 9, then the equation has no solution.
Let's examine each equation:
1) 5v + 3 = 5v - 5
To solve this equation, we can start by subtracting 5v from both sides:
3 = -5
Here, we see that 3 is not equal to -5, which means the equation has no solution.
2) 2x - 4 = 2x + 7 - x
By simplifying the equation, we get:
-4 = 7 - x
To solve for x, we can subtract 7 from both sides:
-11 = -x
Now, we can multiply both sides by -1 to isolate x:
11 = x
Since we obtained a specific value for x, the equation has a solution.
3) 2y + 5 - y = 2y - 3(y - 6)
First, let's distribute the -3:
2y + 5 - y = 2y - 3y + 18
Simplifying further, we get:
y + 5 = -y + 18
To isolate the y terms, we can subtract y from both sides:
5 = -2y + 18
Subtracting 18 from both sides gives us:
-13 = -2y
Dividing both sides by -2, we find:
6.5 = y
Here, we have a specific value for y, so the equation has a solution.
4) 7z + 9 = -7z - 6
By simplifying the equation, we get:
14z = -15
To solve for z, we divide both sides by 14:
z = -15/14
Since we have a specific value for z, the equation has a solution.
Therefore, the equation that has no solution is 5v + 3 = 5v - 5.
To determine which equation has no solution, we need to simplify each equation and see if they lead to a logical inconsistency. Let's go through each option step-by-step:
Option 1: 5v + 3 = 5v – 5
To solve this equation, we can start by subtracting 5v from both sides:
5v + 3 - 5v = 5v - 5 - 5v
3 = -5
This equation leads to a contradiction since 3 cannot be equal to -5. Therefore, this equation has no solution.
Option 2: 2x – 4 = 2x + 7 – x
Let's simplify this equation step-by-step:
2x - 4 = 2x + 7 - x
Combine like terms:
2x - 4 = x + 7
Subtract x from both sides:
2x - x - 4 = x - x + 7
x - 4 = 7
Add 4 to both sides:
x - 4 + 4 = 7 + 4
x = 11
This equation has a solution, which is x = 11.
Option 3: 2y + 5 – y = 2y – 3(y – 6)
Let's simplify this equation step-by-step:
2y + 5 - y = 2y - 3(y - 6)
Combine like terms:
y + 5 = 2y - 3y + 18
Combine like terms again:
y + 5 = -y + 18
Add y to both sides:
y + y + 5 = -y + y + 18
2y + 5 = 18
Subtract 5 from both sides:
2y + 5 - 5 = 18 - 5
2y = 13
Divide by 2:
y = 6.5
This equation has a solution, which is y = 6.5.
Option 4: 7z + 9 = –7z – 6
Let's simplify this equation step-by-step:
7z + 9 = -7z - 6
Add 7z to both sides:
7z + 7z + 9 = -7z + 7z - 6
14z + 9 = -6
Subtract 9 from both sides:
14z + 9 - 9 = -6 - 9
14z = -15
Divide by 14:
z = -15/14
This equation also has a solution, which is z = -15/14.
From the calculations above, we see that the equation with no solution is Option 1: 5v + 3 = 5v – 5.