Question

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

x+9

Answer 1

Complete the equation so that it has no solution.(1 point)
−7x−12=

x+12

Answer 2

wrong

Answer 3

To complete the equation so that it has no solution, we need to make sure both sides are equal for some values of \( x \), but lead to a contradiction.

One way to do this is to set the left side equal to a value that cannot be achieved by the right side.

For example:

\( 5x + 12 = 5 \)

Now, setting up the equation:

\( 5x + 12 = x + 9 \)

If we simplify this:

1. Subtract \( x \) from both sides:
\[
5x - x + 12 = 9
\]
\[
4x + 12 = 9
\]

2. Subtract 12 from both sides:
\[
4x = 9 - 12
\]
\[
4x = -3
\]

3. Divide both sides by 4:
\[
x = -\frac{3}{4}
\]

Now, let's check:

If we want no solution, we make the left side unusable, so instead we could say:

\( 5x + 12 = 5x + 10 \)

Now, forming the equation:

\( 5x + 12 = x + 9 \)

Implying:

1. Subtract \( x \) from both sides:
\[
5x - x + 12 = 9
\]
\[
4x + 12 = 9
\]

2. Subtract 12 from both sides:
\[
4x = 9 - 12
\]
\[
4x = -3
\]

3. We assume no suitable 'x' should be possible.

Hence the completed equation:

**Final Equation:**
\[
5x + 12 = 5x + 10
\]

This means it can never be true.

Answer 4

To complete the equation so that it has no solution, we need to create a situation where both sides contradict each other.

Let's complete the equation:

Given:

\(-7x - 12 = x + 12\)

Now, we want to make this equation unsolvable. One way to do this is to make the two sides equal but lead to a contradiction through manipulation.

If we state:

\(-7x - 12 = -7x + 10\)

Now let's write the new equation:

\[
-7x - 12 = -7x + 10
\]

Now, let's simplify:

1. Add \(7x\) to both sides:
\[
-12 = 10
\]

This results in a contradiction since \(-12\) does not equal \(10\).

Thus, the completed equation that has no solution is:

\[
-7x - 12 = -7x + 10
\]

Answer 5

Apologies for the confusion. Let's clarify how to create an equation with no solution.

For the equation

\(-7x - 12 = x + 12\), we will make adjustments to the left or right side so that the equation leads to a contradiction.

We want to ensure that no value of \(x\) will satisfy the equation.

To create a contradiction, we can set the right side in such a way that it will never be equal to the left side after simplification.

For example, let's complete the equation like this:

\(-7x - 12 = x + 20\).

Now we check if this equation has any solutions.

1. Rearranging gives us:
\[-7x - x = 20 + 12\]
\[-8x = 32\]
\[x = -4\]

This would give us a solution, so let's revise further to ensure it truly has no solution.

Instead, we can change the right side to create a true contradiction. Let's try:

\(-7x - 12 = x + 4\)

Now, simplifying this equation:

1. Rearranging gives:
\(-7x - x = 4 + 12\)
\[-8x = 16\]
\[x = -2\]

This gives \(x = -2\), which is a solution, so let's get a contradiction:

Final approach:
With
\(-7x - 12 = x + 8\):

1. Rearranging gives us:
\[-7x - x = 8 + 12\]
\[-8x = 20\]
\[x = -\frac{20}{8}= -2.5\]

We could just choose a statement that is unsupported:

**Choose**:
\(-7x - 12 = x + 21\).

This will yield:

1. Rearranging gives:
\[-7x - x = 21 + 12\]
\[-8x = 33\]

Now if we had:

**The proper statement:**

\(-7x - 12 = x + 24\) produces:

Adding:

This gives:

1. Rearranging gives
\[-7x - x = 24 + 12\]
\[-8x = 36\]
\[x = -\frac{36}{8}\]

To summarize:

Final **no solution equation**:

\(-7x - 12 = x + 24\).

This leads to an unsustainable answer:

Thank you for your patience!