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

x+9

Answer 1

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:

1. Subtract \( x \) from both sides:

\[ 5x - x + 12 = 9 \]
\[ 4x + 12 = 9 \]

2. Now, subtract 12 from both sides:

\[ 4x = 9 - 12 \]
\[ 4x = -3 \]

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:

1. Subtract \( x \) from both sides:

\[ 5x - x + 12 = 12 \]
\[ 4x + 12 = 12 \]

2. Subtract 12 from both sides:

\[ 4x = 0 \]

3. 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:

1. Subtract \( x \) from both sides:

\[ 5x - x + 12 = 5 \]
\[ 4x + 12 = 5 \]

2. Subtract 12 from both sides:

\[ 4x = 5 - 12 \]
\[ 4x = -7 \]

3. 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:

1. 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.