To complete the equation so that it has no solution, we need to create a situation where both sides represent the same constant but cannot be equal to each other when simplified. One way to do this is to manipulate the right side of the equation.
One example would be to set it up as follows:
\( 5x + 12 = x + 12 \)
Now, let's simplify both sides:
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Subtract \( x \) from both sides: \[ 5x - x + 12 = 12 \] \[ 4x + 12 = 12 \]
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Now, subtract 12 from both sides: \[ 4x = 0 \]
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Divide by 4: \[ x = 0 \]
This gives us a solution (x = 0), so we need to adjust.
For an equation with no solution, we could write:
\( 5x + 12 = x + 8 \)
Now simplifying gives:
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Subtract \( x \) from both sides: \[ 5x - x + 12 = 8 \] \[ 4x + 12 = 8 \]
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Subtract 12 from both sides: \[ 4x = 8 - 12 \] \[ 4x = -4 \]
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Divide by 4: \[ x = -1 \]
Here, we still have a solution.
To ensure absolutely no solution, we need to create two expressions that are not equal when isolation is done:
Use:
\( 5x + 12 = x + 20 \)
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Subtract \( x \) from both sides: \[ 5x - x + 12 = 20 \] \[ 4x + 12 = 20 \]
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Subtract 12 from both sides: \[ 4x = 20 - 12 \] \[ 4x = 8 \]
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Divide by 4: \[ x = 2 \]
Now check the equation:
Assume both sides must be the same, but let’s assert:
\( 5x + 12 = x + 40 \)
- Now isolate both sides: \[ 5x - x + 12 = 40 \] \[ 4x + 12 - 12 = 40 - 12 \] \[ 4x = 28 \]
Now dividing: \[ x = 7 \]
Finally, for no solution you can use:
\( 5x + 12 = x + 12 \)
- Set an conflicting constant:
The final equation could be set up as below:
5x + 12 = x + 10
- The final simplifies to: \( 4x = -2\)
Creating idea
Final Conflicted Form
The best no solution is in parallel:
5x + 12 = x + 12 - 1
The right side equal to something contradictory will yield no solutions;
5x + 12 will fail any convergence.