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Find the missing number so that the equation has no solutions. $\newline$ $-2x - 7 =$ ____ $x + 20$

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Create 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 - 7 =

____

x + 20

Equation with No Solutions: When does an equation have no solutions? $\newline$ 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.
Analysis of Given Equation: Let's analyze the given equation: $\newline$ $-2x - 7 = \_\_\_\_x + 20$ $\newline$ To have no solutions, the coefficients of $x$ must be the same on both sides of the equation, but the constants must be different.
Equate Coefficients of $x$ : Let's equate the coefficients of $x$ on both sides: $\newline$ -2 = ____ $\newline$ The missing number must be $-2$ to have the same coefficients for $x$ .
Check Constants: Now, let's check the constants: $\newline$ $-7 \neq 20$ $\newline$ Since the constants are already different, we have ensured that the equation will have no solutions if the coefficients of $x$ are the same.

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