To solve the inequalities \((–97u–26)/8≥9\) and \((95u+13)/6≥12\), we will solve each inequality separately.
Solving the first inequality:
\[ \frac{-97u - 26}{8} \geq 9 \]
-
Multiply both sides by 8 (since 8 is positive, the inequality direction does not change): \[ -97u - 26 \geq 72 \]
-
Add 26 to both sides: \[ -97u \geq 72 + 26 \] \[ -97u \geq 98 \]
-
Divide both sides by -97 (remember to reverse the inequality): \[ u \leq \frac{98}{-97} \] \[ u \leq -\frac{98}{97} \]
Solving the second inequality:
\[ \frac{95u + 13}{6} \geq 12 \]
-
Multiply both sides by 6 (since 6 is positive, the inequality direction does not change): \[ 95u + 13 \geq 72 \]
-
Subtract 13 from both sides: \[ 95u \geq 72 - 13 \] \[ 95u \geq 59 \]
-
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: \[ u \leq -\frac{98}{97} \quad \text{or} \quad u \geq \frac{59}{95} \]