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

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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

\_\_\_\_x + 20 = -2x + 2

Identifying No Solutions: Understanding when an equation has no solutions. 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.
Analyzing Given Equation: Analyzing the given equation. $\newline$ We have the equation $3x + 20 = -2x + 2$ . To have no solutions, the coefficient of $x$ on both sides must be the same, but the constants must be different.
Equating Coefficients of $x$ : Equating the coefficients of $x$ . To have no solutions, the missing coefficient of $x$ must be equal to $-2$ . So, we replace the blank with $-2$ . $-2x + 20 = -2x + 2$
Checking Constants: Checking the constants. $\newline$ Now, we have $-2x + 20$ on the left side and $-2x + 2$ on the right side. The coefficients of $x$ are the same, but the constants are different ( $20 \neq 2$ ). This confirms that the equation will have no solutions.

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