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Find the missing number so that the equation has no solutions. $\newline$ $\_\_\_\_x - 15 = 4x - 8$

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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 - 15 = 4x - 8

Analyze the equation: Analyze the equation ____x - 15 = 4x - 8 to determine when it has no solutions. $\newline$ An equation has no solutions when the variables on both sides have the same coefficient but the constants are different, making the two sides of the equation never equal.
Compare coefficients of $x$ : Compare the coefficients of $x$ on both sides of the equation. $\newline$ For the equation 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 $4$ . $\newline$ Missing number: $4$
Check constants: Check the constants on both sides of the equation. $\newline$ The constants are $-15$ on the left side and $-8$ on the right side. Since they are different, the equation will have no solutions if the coefficients of $x$ are the same.
Write final equation: Write the final equation with the missing number filled in to confirm that it has no solutions. $\newline$ $4x - 15 = 4x - 8$ $\newline$ Subtract $4x$ from both sides to see if the constants are equal. $\newline$ $-15 = -8$ $\newline$ The constants are not equal, confirming that the equation has no solutions.

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