Complete the equation so that it has no solution
5x + 12 = __x + 9
In order to have no solution, we need to make the equation inconsistent. This means that the equation must be equivalent to a contradiction, such as 0 = 1.
To create a contradiction in the equation, we can subtract the same number from both sides of the equation that eliminates a constant term on one side.
Thus, subtracting 9 from both sides:
5x + 12 - 9 = __x + 9 - 9
5x + 3 = __x + 0
Next, we can eliminate the variable terms on either side of the equation. To create a contradiction, we can choose to eliminate the variable term with the higher coefficient.
Subtracting 5x from both sides:
5x - 5x + 3 = __x - 5x
3 = __x - 5x
We can see that we cannot combine like terms on the right side of the equation since the variable term __x - 5x cannot be simplified.
Thus, the equation has no solution.
fill in the blank so that the equation has no solution.
5x + 12 = __x + 9
To have no solution, we need to create an inconsistency between the two sides of the equation. One way to do this is to have different terms on each side that cannot be simplified or combined.
To accomplish this, we can subtract the same number from both sides that eliminates the terms with variables.
Subtracting 5x from both sides:
5x - 5x + 12 = __x - 5x + 9
This simplifies to:
12 = (__ - 5)x + 9
To create an inconsistency, we want the coefficient of x on the right side to be different from the coefficient of x on the left side.
Let's solve for the coefficient of x on the right side by the equation:
(__ - 5)x = 0x
We need the coefficient of x on the right side to be different from 0. Therefore, filling in the blank with any number other than 5 in "__ - 5" will create an equation with no solution.
For example, filling in the blank with 6:
12 = (6 - 5)x + 9
This simplifies to:
12 = x + 9
To further simplify, we subtract 9 from both sides:
3 = x
So, when the blank is filled with 6, the equation has a solution of x = 3.
However, if we choose any other number for the blank, such as 4, 7, or any value different from 5, the equation will have no solution.
To make the equation have no solution, we need to create an equation where the variables on both sides cancel out. Since we have a 5x on the left side of the equation, we can cancel it out by adding -5x to both sides of the equation.
So, 5x + 12 + (-5x) = __x + 9 + (-5x).
Simplifying this, we get:
12 = -4x + 9.
To cancel out the variable terms on the right side, we can subtract 9 from both sides:
12 - 9 = -4x + 9 - 9.
Simplifying further, we have:
3 = -4x.
To solve for x, we can divide both sides of the equation by -4:
3 / -4 = -4x / -4.
Simplifying once more, we get:
-3/4 = x.
Therefore, the completed equation with no solution is:
5x + 12 = -3/4x + 9.