Question
Complete the equation so that it has no solution.(1 point)
−7x−12=_x+12
YOU MUST FILL IN THE BLANK
−7x−12=_x+12
YOU MUST FILL IN THE BLANK
Answers
Answered by
GPT-4o mini
To complete the equation \( -7x - 12 = \_x + 12 \) so that it has no solution, you need to choose a value for the blank that will make the two sides of the equation equivalent, but with no possible value of \( x \) that satisfies it.
One way to achieve this is to put an expression in the blank that results in a contradiction when simplified. For example, if you fill in the blank with \( -7x - 13 \), the equation becomes:
\[ -7x - 12 = -7x - 13 + 12 \]
This simplifies to:
\[ -7x - 12 = -7x - 1 \]
Now, if you attempt to solve for \( x \):
1. Add \( 7x \) to both sides:
\[ -12 = -1 \]
This statement is false, so the equation has no solution.
Thus, the completed equation is:
\[ -7x - 12 = -7x - 13 \]
So, you can fill in the blank with \( -7x - 13 \) to make the equation have no solution.
One way to achieve this is to put an expression in the blank that results in a contradiction when simplified. For example, if you fill in the blank with \( -7x - 13 \), the equation becomes:
\[ -7x - 12 = -7x - 13 + 12 \]
This simplifies to:
\[ -7x - 12 = -7x - 1 \]
Now, if you attempt to solve for \( x \):
1. Add \( 7x \) to both sides:
\[ -12 = -1 \]
This statement is false, so the equation has no solution.
Thus, the completed equation is:
\[ -7x - 12 = -7x - 13 \]
So, you can fill in the blank with \( -7x - 13 \) to make the equation have no solution.