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Find the missing number so that the equation has no solutions. $\newline$ $\_\_\_\_x + 19 = -2x - 13$

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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 + 19 = -2x - 13

Identify Conditions: Identify the conditions for no solutions. $\newline$ For an equation to have no solutions, the coefficients of the variables must be the same on both sides, but the constants must be different.
Set Up Equation: Set up the equation with the missing number. $\newline$ $\_\_\_\_x + 19 = -2x - 13$ $\newline$ 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 $-2$ .
Determine Missing Number: Determine the missing number. The missing number must be $-2$ to match the coefficient of $x$ on the right side.
Check Constants: Check if the constants are different. $\newline$ The constants are $19$ on the left side and $-13$ on the right side. Since $19$ does not equal $-13$ , the constants are different.
Confirm No Solutions: Confirm that the equation with the missing number filled in has no solutions. $\newline$ $-2x + 19 = -2x - 13$ $\newline$ Since the coefficients of $x$ are the same and the constants are different, this equation has no solutions.

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