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Find the missing number so that the equation has no solutions. $\newline$ $\_\_\_\_x - 18 = 3x + 9$

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Create linear equations with no solutions or infinitely many solutions

Full solution

Q. Find the missing number so that the equation has no solutions.

\newline

\_\_\_\_x - 18 = 3x + 9

Identify Conditions: Identify the conditions for no solutions. $\newline$ For an equation to have no solutions, the coefficients of the variable terms must be equal, but the constants must be 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 - 18 = 3x + 9 $\newline$ 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 $3$ .
Determine Missing Number: Determine the missing number. Since the coefficients must be the same for no solutions, the missing number is $3$ .
Check Constants: Check if the constants are different. $\newline$ The constants are $-18$ on the left side and $+9$ on the right side. Since $-18$ is not equal to $+9$ , the constants are different.
Confirm No Solutions: Confirm that the equation with the missing number filled in has no solutions. $\newline$ $3x - 18 = 3x + 9$ $\newline$ Subtract $3x$ from both sides to see if the constants remain different. $\newline$ $-18 \neq 9$ $\newline$ The constants are still different, so the equation has no solutions.

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