Solve for u.

(–97u–26)/8≥9
Write your answer as a compound inequality with integers, proper fractions, and improper fractions in simplest form.

1 answer

To solve the inequality \(\frac{-97u - 26}{8} \geq 9\), we start by isolating the term involving \(u\).

  1. Multiply both sides by 8 (since 8 is positive, the inequality sign remains the same):

\[ -97u - 26 \geq 72 \]

  1. Next, add 26 to both sides:

\[ -97u \geq 72 + 26 \]

\[ -97u \geq 98 \]

  1. 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 \(-\frac{98}{97}\).

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