To solve the inequality \(-7 (x + 1) > -9 - 5x\), we will first distribute \(-7\) on the left side:
\[ -7x - 7 > -9 - 5x \]
Next, we will isolate \(x\) by first adding \(5x\) to both sides:
\[ -7x + 5x - 7 > -9 \]
This simplifies to:
\[ -2x - 7 > -9 \]
Now, we will add \(7\) to both sides:
\[ -2x > -2 \]
Next, divide both sides by \(-2\). Remember that when we divide by a negative number, the inequality sign will change direction:
\[ x < 1 \]
So the solution to the inequality is:
\[ x < 1 \]