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Complete the equation so that it has no solution.(1 point)

5x+12=____x+9

7 answers

To create an equation with no solution, we want to set it up so that the two sides represent conflicting statements. One way to do this is to make the coefficients of \(x\) on both sides equal while making the constants different.

Let's use the coefficient of \(x\) on the left, which is 5, and set the coefficient on the right also to 5. Then we'll make sure that the constants do not match.

Starting with the equation:

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

To ensure there's no solution, we can choose \(C\) such that:

\[ 12 \neq C \]

So, we can choose \(C = 10\).

The complete equation will be:

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

This leads to:

\[ 12 = 10 \]

which is a contradiction, thus confirming that there is no solution.

so the blank is five

Yes, that's correct! In the equation:

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

you would fill the blank with 5 to complete it as follows:

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

This results in:

\[ 12 = 9, \]

which is a contradiction. Therefore, the equation has no solution. So the blank is indeed filled with 5.

Complete the equation so that it has no solution.(1 point)
−7x−12=_____x+12. And for this one?

To complete the equation \(-7x - 12 = ___x + 12\) so that it has no solution, we need to make the coefficients of \(x\) equal while ensuring that the constant terms create a contradiction.

Starting with the left side, the coefficient of \(x\) is \(-7\). We'll set the coefficient on the right side to also be \(-7\):

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

To make sure there’s no solution, the constants must be different:

\[ -12 \neq C \]

We can choose \(C = 12\). Therefore, we can complete the equation as follows:

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

This gives us:

\[ -12 = 12 \]

This is a contradiction, meaning the equation has no solution. So, the blank should be filled with -7 to achieve this.

Solve for x to determine if the equation has one, none, or infinite solutions.

6(2x+4)−24=12x
Responses

The equation has infinite solutions.
The equation has infinite solutions.

The equation has no solution.
The equation has no solution.

The equation has one solution: x=0
x
=
0
.
The equation has one solution: x equals 0 .

The equation has one solution: x=−20
x
=
−
20
.

Let's solve the equation step by step:

The equation given is:

\[ 6(2x + 4) - 24 = 12x \]

First, distribute the \(6\) on the left side:

\[ 12x + 24 - 24 = 12x \]

Now simplify the left side:

\[ 12x + 0 = 12x \]

This simplifies to:

\[ 12x = 12x \]

Now, this equality holds true for any value of \(x\). This indicates that both sides of the equation are equivalent regardless of the value of \(x\).

Since the equation is true for all real numbers, we conclude that there are infinite solutions.

So, the correct response is:

The equation has infinite solutions.