Question

Solve the inequality. Express the solution set in interval notation. −17<3−5n ≤ 22

Answer 1

The inequality −17<3−5n ≤ 22 is solved by adding 17 to all parts, subtracting 3, and finally dividing by −5, remembering to flip the inequality signs. The solution set in interval notation is [−7.2, −3/5).

Step-by-step explanation:

To solve the inequality −17<3−5n ≤ 22, we first isolate the variable 'n' by executing similar operations on all three parts of the inequality. Let's break this down step by step:

1. Add 17 to all parts of the inequality to cancel the −17 on the left side: 0 < 3 + 17 −5n ≤ 22 + 17.
2. This simplifies to: 0 < 20 −5n ≤ 39.
3. Next, subtract 3 from all parts of the inequality: −3 < 20 − 3 −5n ≤ 39 − 3.
4. Which simplifies to: −3 < 17 −5n ≤ 36.
5. Now, divide all parts of the inequality by −5: −3/−5 < 17/−5 −n ≤ 36/−5.
6. Since dividing by a negative number reverses the inequality, it now reads: −3/5 > n ≥ −7.2.

So, the solution set in interval notation is [−7.2, −3/5).