5a − 2 < 18a < _____

Answer 1

To solve this inequality, we need to isolate the variable 'a' in the middle of the inequality.

Starting with the given inequality, 5a - 2 < 18a, we can first add 2 to both sides:

5a - 2 + 2 < 18a + 2
5a < 18a + 2

Next, we can subtract 18a from both sides:

5a - 18a < 18a + 2 - 18a
-13a < 2

Finally, we divide both sides by -13, remembering to reverse the inequality sign because we are dividing by a negative number:

-13a / -13 > 2 / -13
a > -2/13

So the solution to the inequality is a > -2/13.