Question

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

Item 1

COURSE TOOLS

5x + 12 = Box x+9

Answer 1

To complete the equation \( 5x + 12 = \text{Box} \, x + 9 \) so that it has no solution, we need to create a situation where the left side and right side are parallel lines (i.e., they have the same slope but different intercepts).

The original equation is:

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

For the left side \( 5x + 12 \) and the right side \( \text{Box} \, x + 9 \) to have no solutions, the coefficient of \( x \) on the right side (the Box) must equal the coefficient of \( x \) on the left side (which is 5), but the constant terms must be different.

Thus, if we set:

\[ \text{Box} = 5 \]

and then make sure the constant terms are different (for example, we can set the constant on the right side to be different from 9):

\[ \text{Box} = 5, \quad \text{and substitute a different constant, like 10:} \]

We can render the equation as:

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

Now the equation is:

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

If you try to solve it, you would subtract \( 5x \) from both sides:

\[ 12 = 10 \]

This is a contradiction, thus the equation has no solution. Therefore, we can fill in the Box as:

**Box = 5.**