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.