To solve the equation \(-4(2x - 11) + 7 = 19\), follow these steps:
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Distribute \(-4\) across the terms in the parentheses: \[ -4 \cdot 2x + -4 \cdot -11 = -8x + 44. \] So the equation becomes: \[ -8x + 44 + 7 = 19. \]
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Combine the constants on the left side: \[ 44 + 7 = 51. \] Therefore, the equation simplifies to: \[ -8x + 51 = 19. \]
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Subtract 51 from both sides: \[ -8x + 51 - 51 = 19 - 51, \] resulting in: \[ -8x = -32. \]
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Now, divide both sides by \(-8\): \[ x = \frac{-32}{-8} = 4. \]
Thus, the solution is: \[ \boxed{4}. \]