Ask a New Question
Menu

Complete the following equation so that it has no solutions, simplify:

5x-4=

1 answer

To create an equation that has no solutions, we can manipulate the equation so that both sides effectively represent contradictory statements.

One way to do this is to set the expression on one side to a number, and the other side to a different number that cannot be true.

For example:

  1. Start with:
    \( 5x - 4 = 3 \)

  2. Now let's simplify this equation to show that there's a contradiction:

    • Move \( -4 \) to the right side:
      \( 5x = 3 + 4 \)
      \( 5x = 7 \)
      \( x = \frac{7}{5} \)
      (This has a solution.)

  3. Instead, let's make it different:
    \( 5x - 4 = 5x + 1 \)

  4. Now simplify:

    • Subtract \( 5x \) from both sides:
      \( -4 = 1 \)

This is a contradiction because -4 does not equal 1. Therefore, the equation \( 5x - 4 = 5x + 1 \) has no solutions.

So, the completed equation is:

5x - 4 = 5x + 1.
This equation simplifies to an impossibility (-4 = 1), showing there are no solutions.