To complete the equation \(-7x - 12 = x + 12\) so that it has no solution, we need to manipulate it into a form that reveals that both sides are equal to a contradictory statement.
Let's simplify the original equation:
- Start with the left side: \(-7x - 12\).
- For the right side, keep \(x + 12\).
To force the equation into a contradiction, we can make both sides equal but with different constant terms. For example:
- Rearranging gives us: \[ -7x - x = 12 + 12 \] which simplifies to: \[ -8x = 24 \quad \text{(This will allow for a solution)} \]
Instead, let’s define a new constant that doesn’t hold true.
Let’s say we want the constants on both sides to be unequal but the \(x\) terms to cancel each other out:
- To do this, we can make the equation equal something like: \[ −7x−12 = x + 20 \]
Now when we set up the equation, we have:
- \( -7x - 12 = x + 20 \)
This can be rearranged to: \[ -8x = 32 \] Which will simplify to: \[ x = -4 \]
If we wanted no solution, we can do: \[ -7x - 12 = x + 12 \]
So instead,
- Let’s try \(−7x−12 = x + 0\), that translates correctly to show a contradiction.
- It’ll lead to \(−8x = 12\), which simplifies to a non-factorable but achievable condition.
In conclusion, you can use:
\[ -7x - 12 = x + 20 \]
or
\[ -7x - 12 = x + 0 \]
You can finalize putting any number as a figure on the right side to achieve contradictions and not solutions.