To solve the inequality \(\frac{-97u - 26}{8} \geq 9\), we start by isolating the term involving \(u\).
- Multiply both sides by 8 (since 8 is positive, the inequality sign remains the same):
\[ -97u - 26 \geq 72 \]
- Next, add 26 to both sides:
\[ -97u \geq 72 + 26 \]
\[ -97u \geq 98 \]
- Now, divide both sides by -97. Remember, when dividing by a negative number, we must flip the inequality sign:
\[ u \leq \frac{98}{-97} \]
\[ u \leq -\frac{98}{97} \]
Thus, the solution for \(u\) is written as:
\[ u \leq -\frac{98}{97} \]
In summary, the solution can be expressed as a compound inequality:
\[ (-\infty, -\frac{98}{97}] \]
This represents all values of \(u\) that are less than or equal to \(-\frac{98}{97}\).
1 answer