To create an equation with no solution, you can set the two sides of the equation to be equal but contradictory.
For example, if you have:
\[ 5x + 12 = x + 9 \]
You can manipulate it as follows:
- Subtract \( x \) from both sides:
\[ 5x - x + 12 = 9 \] \[ 4x + 12 = 9 \]
- Now, subtract 12 from both sides:
\[ 4x = 9 - 12 \] \[ 4x = -3 \]
- Finally, divide by 4:
\[ x = -\frac{3}{4} \]
If we want no solution, we can make an equation such that the coefficients yield a contradiction when we attempt to solve it.
For instance, if we set:
\[ 5x + 12 = x + 12 \]
Now if we simplify:
- Subtract \( x \) from both sides:
\[ 5x - x + 12 = 12 \] \[ 4x + 12 = 12 \]
- Subtract 12 from both sides:
\[ 4x = 0 \]
- Divide by 4:
\[ x = 0 \]
This is a solution. So let's set up an equation that looks similar but contradicts:
You can set:
\[ 5x + 12 = x + 5 \]
If we rearrange this:
- Subtract \( x \) from both sides:
\[ 5x - x + 12 = 5 \] \[ 4x + 12 = 5 \]
- Subtract 12 from both sides:
\[ 4x = 5 - 12 \] \[ 4x = -7 \]
- Now divide by 4:
\[ x = -\frac{7}{4} \]
With proper coefficients, if we wanted no solution, you could set it with the same left-hand side but contradictory right-hand side.
For example, you could have:
\[ 5x + 12 = 5x + 8 \]
In this case:
- Subtract \( 5x \) from both sides:
\[ 12 = 8 \]
This is a contradiction, hence the equation:
\[ 5x + 12 = 5x + 8 \] has no solution.
So, to complete your equation:
5x + 12 = 5x + 8
This equation has no solution.