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Find the missing number so that the equation has no solutions. $\newline$ $2x - 2 = \underline{\hspace{1cm}}x - 6$

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Create linear equations with no solutions or infinitely many solutions

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Q. Find the missing number so that the equation has no solutions.

\newline

2x - 2 = \underline{\hspace{1cm}}x - 6

Understand No Solutions: Understand when an equation has no solutions. An equation has no solutions when the two sides of the equation are parallel lines, which means the coefficients of $x$ are the same, but the constants are different.
Identify Coefficients and Constants: Identify the coefficients and constants in the given equation. $\newline$ In the equation $2x - 2 = \_\_\_\_x - 6$ , the coefficient of $x$ on the left side is $2$ , and the constant is $-2$ . On the right side, the coefficient of $x$ is missing, and the constant is $-6$ .
Determine Missing Coefficient: Determine the missing coefficient for the equation to have no solutions. $\newline$ Since the equation should have no solutions, the coefficients of $x$ on both sides must be the same, and the constants must be different. We already have the coefficient of $x$ as $2$ on the left side, so the missing coefficient on the right side must also be $2$ .
Verify Different Constants: Verify that the constants are different. $\newline$ The constants are $-2$ on the left side and $-6$ on the right side. Since they are different, the equation will have no solutions with the missing coefficient being $2$ .

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