-1\5x-16>32 2\5

Answer 1

To solve the inequality \(-\frac{1}{5}x - 16 > \frac{32}{5}\), follow these steps:

1. Isolate the term with \(x\): \[ -\frac{1}{5}x - 16 > \frac{32}{5} \] Add \(16\) to both sides: \[ -\frac{1}{5}x > \frac{32}{5} + 16 \] Convert \(16\) into fifths: \[ 16 = \frac{80}{5} \] Now, add: \[ -\frac{1}{5}x > \frac{32}{5} + \frac{80}{5} = \frac{112}{5} \]

2. Multiply both sides by \(-5\): Remember that when you multiply or divide by a negative number, you must flip the inequality sign: \[ x < -5 \cdot \frac{112}{5} \] Simplifying the right side: \[ x < -112 \]

3. Final Answer: \[ x < -112 \]

So the solution to the inequality is \(x < -112\).