Solve for u.

Question

(–97u–26)/8≥9 or (95u+13)/6≥12
Write your answer as a compound inequality with integers, proper fractions, and improper fractions in simplest form.

Answer 1

To solve the inequalities \((–97u–26)/8≥9\) and \((95u+13)/6≥12\), we will solve each inequality separately.

Solving the first inequality:

\[ \frac{-97u - 26}{8} \geq 9 \]

1. Multiply both sides by 8 (since 8 is positive, the inequality direction does not change): \[ -97u - 26 \geq 72 \]

2. Add 26 to both sides: \[ -97u \geq 72 + 26 \] \[ -97u \geq 98 \]

3. Divide both sides by -97 (remember to reverse the inequality): \[ u \leq \frac{98}{-97} \] \[ u \leq -\frac{98}{97} \]

Solving the second inequality:

\[ \frac{95u + 13}{6} \geq 12 \]

1. Multiply both sides by 6 (since 6 is positive, the inequality direction does not change): \[ 95u + 13 \geq 72 \]

2. Subtract 13 from both sides: \[ 95u \geq 72 - 13 \] \[ 95u \geq 59 \]

3. Divide both sides by 95: \[ u \geq \frac{59}{95} \]

Writing the final answer:

Now we combine the results from both inequalities. The solution is: \[ u \leq -\frac{98}{97} \quad \text{or} \quad u \geq \frac{59}{95} \]

Thus, the final answer as a compound inequality is: \[ u \leq -\frac{98}{97} \quad \text{or} \quad u \geq \frac{59}{95} \]