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

5x+12= BLANKx+9

7 answers

To create an equation with no solution, we need to set up an equation where the two sides are parallel and hence never equal.

One way to do this is by ensuring that the coefficients of \( x \) on both sides are the same but the constant terms are different.

For the equation:

\[ 5x + 12 = \text{BLANK}x + 9 \]

We can choose the blank to be 5 (to match the coefficient of \( x \) on the left side) and then select a constant that does not equal 12 when added to 9. For example:

Choose the blank to be 5.

Then we have:

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

This simplifies to:

\[ 12 = 9 \]

Which is a contradiction and thus has no solution.

So, the complete equation is:

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

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

6(2x+4)−24=12x

Let's solve the equation step by step:

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

First, distribute the 6 on the left side: \[ 12x + 24 - 24 = 12x \]

Now, simplify the left side: \[ 12x = 12x \]

Now, we notice that both sides are equal, which means the equation holds true for all values of \( x \). Therefore, the solution set is infinite.

In conclusion, the equation has infinite solutions.

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

9(x+1)=3(5x+1)−12

Let's solve the equation step by step:

Given: \[ 9(x + 1) = 3(5x + 1) - 12 \]

First, distribute the numbers on both sides:

On the left side: \[ 9(x + 1) = 9x + 9 \]

On the right side: \[ 3(5x + 1) - 12 = 15x + 3 - 12 = 15x - 9 \]

Now, we have: \[ 9x + 9 = 15x - 9 \]

Next, let's get all terms involving \( x \) on one side and constant terms on the other side. We can subtract \( 9x \) from both sides: \[ 9 = 15x - 9x - 9 \]

This simplifies to: \[ 9 = 6x - 9 \]

Now, add 9 to both sides: \[ 9 + 9 = 6x \] \[ 18 = 6x \]

Now, divide by 6: \[ x = 3 \]

Thus, the equation has one solution, and that solution is: \[ x = 3 \]

Which of the following is an example of an equation with no solution?(1 point)
Responses

3x+4=3x+4
3 x plus 4 equals 3 x plus 4

4x+3=3x+3
4 x plus 3 equals 3 x plus 3

3x+4=4x+3
3 x plus 4 equals 4 x plus 3

3x+4=3x+3

To determine which of the provided equations has no solution, we can analyze each option:

  1. \( 3x + 4 = 3x + 4 \)
    This simplifies to a true statement (both sides are equal), which means it has infinite solutions.

  2. \( 4x + 3 = 3x + 3 \)
    Rearranging gives \( 4x - 3x = 3 - 3 \) or \( x = 0 \). This equation has one solution.

  3. \( 3x + 4 = 4x + 3 \)
    Rearranging gives \( 3x - 4x = 3 - 4 \) or \( -x = -1 \), which simplifies to \( x = 1 \). This equation has one solution.

  4. \( 3x + 4 = 3x + 3 \)
    Rearranging this gives \( 3x - 3x = 3 - 4 \) or \( 0 = -1 \). This is a contradiction and has no solution.

The correct answer is: \( 3x + 4 = 3x + 3 \), which is an example of an equation with no solution.