Complete the equation so that it has no solution. 5x+12= x+9

Answer 1

To complete the equation \(5x + 12 = x + 9\) so that it has no solution, we need to manipulate it in a way that creates a contradiction.

Let's start with the original equation:

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

Now, we can move \(x\) from the right side to the left side:

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

This simplifies to:

\[ 4x + 12 = 9 \]

Next, we can isolate \(4x\):

\[ 4x = 9 - 12 \]

Which simplifies to:

\[ 4x = -3 \]

Dividing both sides by 4 gives us:

\[ x = -\frac{3}{4} \]

Now we want to adjust the equation to ensure it has no solutions. A common way to do this is to set it up so that the left-hand side (LHS) and right-hand side (RHS) are equal but lead to a false statement.

One way to achieve this is to introduce a term that cancels out:

Let's manipulate the equation so that both sides equal a contradictory statement, for example:

\[ 5x + 12 = x + 9 + k \]

where \(k\) is a constant that ensures the equation is always false. Let's take \(k = 3\):

So we modify the equation to:

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

Now simplify:

The left side simplifies to \(5x + 12\) while the right becomes \(x + 12\). So

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

Subtract \(x + 12\) from both sides:

\[ 5x + 12 - (x + 12) = 0 \]

This simplifies to:

\[ 5x - x + 12 - 12 = 0 \] \[ 4x = 0 \]

This leads to:

\[ x = 0 \]

To create an equation with no solution, you could create a scenario where both sides don't balance at any point. For the case of no solutions, we can change the constant on the right side to ensure the two sides are parallel.

So let's rewrite it as: \[ 5x + 12 = x + 9 + 3 \]

That leads to:

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

This expression reduces to \(5x = x\), or \(4x = 0\), thus giving a solution, but if we state:

\[ 5x + 12 = x + 12 + 3 \]

The whole side would yield:

\[ 5x + 12 = x + 15 \]

So now rearranging:

\[ 5x - x + 12 - 15 = 0 \]

yields:

\[ 4x - 3 = 0 \rightarrow no solution \]

Thus \( \text{Final Version: } 5x + 12 = x + 15 \) yields no solution.

Answer 2

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

Answer 3

To complete the equation \(5x + 12 = (\text{number})x + 9\) such that it has no solution, we need to ensure that the coefficient of \(x\) on the left side is not equal to the coefficient of \(x\) on the right side.

To make the equation have no solution, we can set it up so that the lines represented by both sides are parallel. In mathematical terms, this means that the coefficients of \(x\) must be the same, but the constants must differ.

Given \(5x + 12 = (\text{number})x + 9\), we want:

1. The coefficient of \(x\) on the left is \(5\).
2. The coefficient of \(x\) on the right must be the same, \(5\).
3. We want the constants \(12\) and \(9\) to lead to a contradiction.

So, we can set the number on the right side to \(5\) and then modify the constants.

Let's change the equation to:

\[ 5x + 12 = 5x + k \]

For the equation to have no solutions, we want \(k\) (the constant on the right) to differ from \(12\). Thus, let's choose any value for \(k\) that is not \(12\). For example, let's take \(k = 10\):

So the equation becomes:

\[ 5x + 12 = 5x + 10 \]

This simplifies to:

\[ 12 = 10 \]

Since this is a contradiction, the equation has no solution.

In conclusion, the completed equation that has no solution is:

\[ 5x + 12 = 5x + 10 \]