Solve for u.

Question

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

Answer 1

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

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

$$-97u-26\ge 72$$

2. Next, add 26 to both sides:

$$-97u\ge 72+26$$

$$-97u\ge 98$$

3. Now, divide both sides by -97. Remember, when dividing by a negative number, we must flip the inequality sign:

$$u\le \frac{98}{-97}$$

$$u\le -\frac{98}{97}$$

Thus, the solution for $u$ is written as:

$$u\le -\frac{98}{97}$$

In summary, the solution can be expressed as a compound inequality:

$$(-\mathrm{\infty },-\frac{98}{97}]$$

This represents all values of $u$ that are less than or equal to $-\frac{98}{97}$.