Complete the equation so that it has no solution.(1 point)
5x+12= _ x+9
To create a linear equation with no solution, we can set the coefficients of the variables on both sides of the equation to be equal but set the constant terms to be different.
In this case, to create an equation with no solution, we need to make the coefficients of x on both sides of the equation equal. To do this, we need to multiply the entire equation by a number such that the coefficient of x on both sides becomes 5.
Starting with the given equation:
5x + 12 = _x + 9
We can multiply both sides of the equation by 5 to make the coefficients of x equal:
5(5x + 12) = 5(_x + 9)
25x + 60 = 5x + 45
Now, let's simplify the equation:
25x + 60 = 5x + 45
Next, we can subtract 5x from both sides of the equation to isolate the variable:
25x - 5x + 60 = 5x - 5x + 45
20x + 60 = 45
Now we can subtract 60 from both sides:
20x + 60 - 60 = 45 - 60
20x = -15
Lastly, we can divide both sides of the equation by 20 to solve for x:
(20x)/20 = (-15)/20
x = -15/20
x = -3/4
Therefore, when the equation is completed as:
5x + 12 = 5x + 9
There is no solution, as both sides become equal (5x) and the constants (12 and 9) are different.
In order for the equation to have no solution, we need to eliminate x on one side of the equation.
To do this, we can subtract x from both sides:
5x - x + 12 = 9
This simplifies to:
4x + 12 = 9
Now, we can subtract 12 from both sides:
4x = 9 - 12
This simplifies to:
4x = -3
Finally, to solve for x, we divide both sides by 4:
x = -3/4
Bot the question is Complete the equation so that it has no solution.(1 point)
5x+12= __x+9 Fill out the blank.
To find the value that should replace the blank, we need to create an equation with no solution. In order to do that, we can set the coefficients of both terms involving x to be equal, while the constants on both sides of the equation are not equal.
Therefore, to complete the equation so that it has no solution, we can set the value to -12.
The equation becomes:
5x + 12 = -12x + 9