Question

Complete the equation so that it has no solution.(1 point) 5x+12= x+9 please

Answer 1

To modify the equation \(5x + 12 = x + 9\) so that it has no solution, we can manipulate it so that both sides become equal in a way that cannot occur.

For example, one way to do this is to create a false statement by ensuring the constants or coefficients lead to a contradiction.

A simple alteration could be:
\[5x + 12 = x - 5.\]

This can be solved to see it has no solutions:

1. Rearranging gives:
\[5x - x + 12 + 5 = 0\]
\[4x + 17 = 0\]
\[4x = -17\]
\[x = -\frac{17}{4}.\]

This equation is solvable, so let's try an alternative.

Instead, we can set the equation such that both sides are equal but don't actually exist, for example:

\[5x + 12 = 5.\]

This would imply the solution:
\[5x + 12 = 5\]
\[5x = 5 - 12\]
\[5x = -7\]
\[x = -\frac{7}{5}.\]

### Final Adjustment

Now changing it to:
\[5x + 12 = x + 12.\]
In this case, reducing gives \(4x = 0\) so \(x = 0\), and we adjust to
\[5x + 12 = 5x + 1.\]

Reduction leads to \(12 ≠ 1\), which is a contradiction thus proving:
\[ 5x + 12 = 5x + 1. \]
This equation has no solution because it simplifies to \(12 = 1\) which is false.