To solve the inequality \( -(5d + 4) + (d - 7) < 0 \), we can first simplify the left-hand side:
Distribute the negative sign: \[ -5d - 4 + d - 7 < 0 \]
Combine like terms: \[ (-5d + d) + (-4 - 7) < 0 \] \[ -4d - 11 < 0 \]
Now, isolate \( d \) by adding 11 to both sides: \[ -4d < 11 \]
Next, divide both sides by -4. Remember, when dividing by a negative number, we need to reverse the inequality: \[ d > \frac{11}{-4} \] \[ d > -\frac{11}{4} \]
Thus, the solution to the inequality is: \[ d > -\frac{11}{4} \]