Complete the equation so that it has no solution. 5x + 12 = ___x + 9.
To make the equation have no solution, we need to make the equation contradictory. This means that we want to have a situation where no value of x can simultaneously satisfy both sides of the equation.
To do this, we can start by subtracting x from both sides of the equation:
5x + 12 - x = x + 9 - x
This simplifies to:
4x + 12 = 9
Next, we want to make both sides of the equation unequal, so we can subtract a different number than 12 from both sides. Let's subtract 10 from both sides:
4x + 12 - 10 = 9 - 10
This simplifies to:
4x + 2 = -1
At this point, we have an equation where the left side is 4x + 2 and the right side is -1. Since we want the equation to have no solution, we want the left side and the right side to be unequal no matter what value of x we substitute in.
To achieve this, we can subtract 4x from both sides:
4x + 2 - 4x = -1 - 4x
This simplifies to:
2 = -1 - 4x
Now we have an equation that states 2 equals -1 minus 4x. Since we want the equation to have no solution, we must have an equality that is false, without any x value satisfying it. By comparing the two numbers, 2 and -1, it is clear that this is the case.
Therefore, the equation 5x + 12 = 4x + 9 has no solution when we complete it as 4x + 2 = -1 - 4x.
Complete the equation so that it has no solution. FILL THE BLANK IN. 5x + 12 = ____x + 9.
To make the equation have no solution, we want the coefficients of x on each side of the equation to be different. To achieve this, we can choose any number that is not equal to 5.
So, the missing number would be any number that is not equal to 5, such as 6, 7, 8, 9, or any other number except for 5.
For example, if we choose 6, the completed equation would be:
5x + 12 = 6x + 9.
Since the coefficients of x on each side are different, this equation will have no solution.