Question
Complete the equation so that it has no solution.(1 point)
−7x−12= x+12
To have no solution, the two sides of the equation should be equal but they also should not be equal. In other words, they should contradict each other. To achieve this, we can add x to both sides of the equation:
−7x − 12 + x = x + 12 + x
This simplifies to:
-6x - 12 = 2x + 12
To further contradict the equation, we can add 6x to both sides:
-6x - 12 + 6x = 2x + 12 + 6x
This simplifies to:
-12 = 8x + 12
To contradict even more, we can subtract 12 from both sides:
-12 - 12 = 8x + 12 - 12
This simplifies to:
-24 = 8x
Finally, to find the value of x, we can divide both sides of the equation by 8:
-24 / 8 = 8x / 8
This simplifies to:
-3 = x
So, the equation -7x - 12 = x + 12 has no solution.
To make the equation have no solution, we need to create an equation that has no common solutions for both sides.
To accomplish this, we can solve the equation by combining like terms and isolating the variable:
Starting with the given equation:
-7x - 12 = x + 12
Adding 7x to both sides to eliminate the negative 7x on the left side:
-7x + 7x - 12 = x + 7x + 12
Simplifying:
-12 = 8x + 12
Subtracting 12 from both sides:
-12 - 12 = 8x + 12 - 12
Simplifying:
-24 = 8x
Dividing by 8 to solve for x:
-24/8 = 8x/8
Simplifying:
-3 = x
So, the value of x is -3.
Since we found a solution for x, this means that the equation does have a solution. Therefore, the original equation cannot be completed to have no solution.