Complete the equation so that it has no solution.(1 point)
−7x−12= __x+12
-7x - 12 = -7x + 12
To create an equation that has no solution, we need to make sure that both sides of the equation cannot be equal to each other no matter what value we assign to the variable.
To eliminate the variable on the right side, we can combine like terms:
-7x - 12 = __x + 12
Rearranging the equation, we have:
-7x - __x = 12 + 12
To eliminate the terms with "x," we can combine them:
-7x - __x = 24
Now, we can simplify the left side by combining the x terms:
(-7 - __)x = 24
Since we want the equation to have no solution, we need to make sure that the x terms on the left side cancel out, meaning the coefficients sum to zero.
Therefore, we want to choose a value of __ that makes the equation -7 - __ = 0.
Solving for __:
-7 - __ = 0
Adding 7 to both sides:
-7 + 7 - __ = 0 + 7
Simplifying:
-__ = 7
To find the value of __, we multiply both sides by -1:
-1 * -__ = -1 * 7
Simplifying:
__ = -7
Therefore, to create an equation with no solution, the complete equation is:
-7x - 7 = x + 12
To make the equation have no solution, you need to find a value to replace the blank that will make the equation inconsistent or contradictory.
In this case, we have −7x − 12 = __x + 12. To create an inconsistent equation, we need to eliminate the variable from one side of the equation.
First, let's simplify the equation by combining like terms on both sides.
We can add 7x to both sides to eliminate the x term on the left side. This gives us:
−7x + 7x − 12 = __x + 7x + 12
Simplifying further, we have:
-12 = 8x + 12
To eliminate the constant term on the right side, we can subtract 12 from both sides:
-12 - 12 = 8x + 12 - 12
Simplifying further, we have:
-24 = 8x
Now, we can divide both sides by 8 to solve for x:
(-24) / 8 = 8x / 8
Simplifying further, we have:
-3 = x
So, the completed equation that has no solution is:
−7x − 12 = -3x + 12