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Find the missing number so that the equation has no solutions. $\newline$ $-3x - 15 = \_\_\_\_x - 16$

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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

-3x - 15 = \_\_\_\_x - 16

Understand Parallel Lines: To determine the missing number that would result in no solutions, we need to understand that no solutions occur when the equations are parallel lines, which means the coefficients of $x$ must be the same, but the constants must be different.
Ensure Same Coefficients: The coefficient of $x$ on the left side of the equation is $-3$ . For the equation to have no solutions, the coefficient of $x$ on the right side must also be $-3$ .
Compare Constants: Now, let's compare the constants. On the left side, we have $-15$ , and on the right side, we have $-16$ . Since these constants are already different, we can conclude that if the coefficients of $x$ are the same, the equation will have no solutions.
Identify Missing Number: Therefore, the missing number that makes the coefficient of $x$ on the right side equal to $-3$ is $-3$ itself. This ensures that the equation $-3x - 15 = -3x - 16$ has no solutions because it represents two parallel lines that never intersect.

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