Question

Please solve and explain how to solve the compound inequality:

4 < 4a +3 < 18

Answer 1

a compound inequality is just two inequalities. Solve each one.

4 < 4a+3
1 < 4a
1/4 < a

4a+3 < 18
4a < 15
a < 15/4

so, the solution is

1/4 < a < 15/4

or, you can indeed solve it as a combination, if it's relatively simple, as this one is.

4 < 4a+3 < 18
subtract 3 all across
1 < 4a < 15
divide by 4
1/4 < a < 15/4