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Find the missing number so that the equation has no solutions. $\newline$ $\_\_\_\_x + 11 = -3x + 6$

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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

\_\_\_\_x + 11 = -3x + 6

Identify No Solutions: Analyze the equation for no solutions. An equation has no solutions when the coefficients of the variable terms are equal, but the constants are different. This creates parallel lines when graphed, which means they will never intersect.
Set Up Equation: Set up the equation with the missing number. $\newline$ $\_\_\_\_x + 11 = -3x + 6$ $\newline$ To have no solutions, the coefficient of $x$ on the left side must be the same as the coefficient of $x$ on the right side, which is $-3$ .
Equalize Coefficients: Make the coefficients of $x$ equal. $\newline$ The missing number must be $-3$ to match the coefficient on the right side. $\newline$ $-3x + 11 = -3x + 6$
Check Constants: Check if the constants are different. $\newline$ The constants are $11$ and $6$ . Since they are different, the equation will have no solutions.
Confirm No Solutions: Confirm that the equation has no solutions. $\newline$ Since the coefficients of $x$ are the same and the constants are different, the equation $-3x + 11 = -3x + 6$ has no solutions.

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