Question

Complete the following equation so that it has no solutions:
5x-4=

Answer 1

To make the equation \(5x - 4 = k\) have no solutions, you can set \(k\) to be a value that is impossible for \(5x - 4\) to equal.

For example, if you set:

\[
5x - 4 = 5
\]

In this case, rearranging gives:

\[
5x = 9 \\
x = \frac{9}{5}
\]

This has a solution. However, if you want to ensure there are no solutions, one method is to set the right side to something that is inconsistent with the left side.

A simple way to do this is to set:

\[
5x - 4 = 5x + 1
\]

Rearranging gives:

\[
-4 = 1
\]

This statement is false and therefore has no solutions.

Alternatively, you could also set:

\[
5x - 4 = -4
\]

which yields:

\[
5x = 0 \\
x = 0
\]

This has a solution, so you would need a contradiction.

So a final valid example where the left and right sides are never equal would be:

\[
5x - 4 = 5x - 5
\]

This gives:

\[
-4 = -5
\]

This is false, indicating that the equation has no solutions.