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Find the missing number so that the equation has no solutions. $\newline$ $2x - 3 = \underline{\quad}x - 10$

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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

2x - 3 = \underline{\quad}x - 10

Understand Equation Solutions: Understand 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.
Identify Coefficients and Constants: Identify the coefficients and constants in the given equation. $\newline$ In the equation $2x - 3 = \_\_\_\_x - 10$ , the coefficient of $x$ on the left side is $2$ , and the constant is $-3$ . On the right side, the coefficient of $x$ is missing, and the constant is $-10$ .
Determine Missing Number: Determine the missing number for the equation to have no solutions. $\newline$ For the equation to have no solutions, the coefficients of $x$ must be the same on both sides, but the constants must be different. Since the left side has a coefficient of $2$ , the missing number for the coefficient of $x$ on the right side must also be $2$ .
Check for Errors: Check for any mathematical errors. $\newline$ The equation $2x - 3 = 2x - 10$ has the same coefficients for $x$ (which are $2$ ) but different constants ( $-3$ and $-10$ ). This means the lines represented by each side of the equation are parallel and will never intersect, confirming that the equation has no solutions.

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