Solve the inequality for \( x \). \[ 7 x-35<-4(2-4 x) \] Simplify your answer as much as possible. \( \square \) \( \square>\square \) \( \square \leq \square \) \( \square \geq \square \) 믐

First, let's solve the inequality step by step. Starting from the given inequality: \[ 7x - 35 < -4(2 - 4x) \] Distributing \(-4\) on the right side: \[ 7x - 35 < -8 + 16x \] Now, let's get all the \(x\) terms on one side and the constant terms on the other. Subtract \(7x\) from both sides: \[ -35 < -8 + 16x - 7x \] This simplifies to: \[ -35 < -8 + 9x \] Next, add \(8\) to both sides: \[ -35 + 8 < 9x \] This simplifies to: \[ -27 < 9x \] Now, divide both sides by \(9\) (remembering to reverse the inequality if we were dividing by a negative, which we're not in this case): \[ -\frac{27}{9} < x \] This simplifies to: \[ -3 < x \] or equivalently: \[ x > -3 \] In conclusion, the solution to the inequality is: \[ x > -3 \]