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Find the missing number so that the equation has no solutions. $\newline$ $-4(-x + 8) = -3(2x + 7) + \_\_\_\_x + 9$

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Multiply two binomials: special cases

Full solution

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

\newline

-4(-x + 8) = -3(2x + 7) + \_\_\_\_x + 9

Distribute Terms: Distribute the $-4$ and $-3$ across the terms inside the parentheses. $\newline$ $-4(-x + 8) = -4(-x) + 4(8)$ $\newline$ $-3(2x + 7) = -3(2x) - 3(7)$ $\newline$ Simplified: $4x - 32 = -6x - 21 + \_\_\_\_x + 9$
Combine Like Terms: Combine like terms on the right side of the equation. $\newline$ $-6x + \_\_\_\_x - 21 + 9$ $\newline$ Simplified: $(-6 + \_\_\_\_x)x - 12$
Set Coefficients Equal: Set the equation to have no solutions by making the coefficients of $x$ equal on both sides and the constants not equal. $\newline$ $4x - 32 = (-6 + \_\_\_\_x)x - 12$ $\newline$ For no solutions, $4 = -6 + \_\_\_\_x$ and $-32 \neq -12$
Solve for x: Solve for the missing number ____x.4 = -6 + ____x____x = 4 + 6____x = 10

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