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Find the missing number so that the equation has no solutions. $\newline$ $\_\_\_\_x - 7 = 2x + 17$

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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 - 7 = 2x + 17

Analyze Equation: Analyze the equation to understand when it has no solutions. An equation has no solutions when the coefficients of the variable terms are the same on both sides, but the constants are different. This creates a contradiction.
Set Up Equation: Set up the equation with the missing number. $\newline$ ____x - 7 = 2x + 17 $\newline$ To have no solutions, the coefficient of $x$ on the left side must be the same as the coefficient on the right side, which is $2$ .
Determine Missing Number: Determine the missing number. Since the coefficients must be the same for no solutions, the missing number is $2$ .
Check Constants: Check if the constants are different. $\newline$ On the left side, the constant is $-7$ , and on the right side, it is $+17$ . Since $-7$ does not equal $+17$ , the constants are different.
Confirm No Solutions: Confirm that the equation with the missing number filled in has no solutions. $\newline$ $2x - 7 = 2x + 17$ $\newline$ Subtract $2x$ from both sides to see if the constants are indeed different. $\newline$ $-7 \neq 17$ $\newline$ This confirms that the equation has no solutions.

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