Complete the equation so that it has no solution. 5x + 12 =_x+9
5x + 12 ≠ 5x + 9
To make the equation have no solution, we need to create a contradiction. Let's proceed step by step:
Step 1: Combine like terms on both sides of the equation:
5x + 12 = _x + 9
Step 2: Since we want to create a contradiction, we can multiply both sides of the equation by -1 to change the signs of all the terms:
-1(5x + 12) = -1(_x + 9)
This gives us:
-5x - 12 = -_x - 9
Step 3: Now, we can simplify and combine like terms again on both sides:
-5x - 12 = -_x - 9
Step 4: To create a contradiction, let's subtract -x from both sides of the equation:
-5x - 12 - (-_x) = -_x - 9 - (-_x)
Simplifying further:
-5x - 12 + x = -x - 9 + x
Step 5: Combine like terms once again:
-4x - 12 = -9
Step 6: Now, add 9 to both sides of the equation in order to isolate -4x:
-4x - 12 + 9 = -9 + 9
Simplifying the equation gives us:
-4x - 3 = 0
Step 7: Finally, add 3 to both sides to isolate -4x:
-4x - 3 + 3 = 0 + 3
Simplifying further:
-4x = 3
Step 8: Divide both sides of the equation by -4 to solve for x:
-4x / -4 = 3 / -4
This gives us:
x = -3/4
Therefore, by completing the equation as 5x + 12 = -x + 9, we obtain the solution x = -3/4, not a contradiction. Hence, it does not have no solution.
To create an equation with no solution, we need to find values that would make the equation inconsistent. In other words, we want to find the value of "_x" that would lead to a contradiction.
Given the equation 5x + 12 = _x + 9, we can begin by simplifying the equation on both sides:
Subtracting _x from both sides, we have: 5x + 12 - _x = 9
Then, combining like terms, we get: 4x + 12 = 9
To proceed, we need to isolate the variable x. Let's subtract 12 from both sides to get rid of the constant term:
4x + 12 - 12 = 9 - 12
4x = -3
Now, let's solve for x by dividing both sides of the equation by 4:
4x/4 = -3/4
x = -3/4
So, to complete the equation 5x + 12 = _x + 9 with no solution, we would need to fill in any value for _x that is NOT equal to -3/4. For example, we can choose any real number except -3/4 as the value of _x, such as _x = 1.