Question

How do you solve 4x + 1 ≤ 17 and 5x - 1 > 19?

Answer 1

This compound inequality has no solutions.

Explanation:

To solve a compound inequality consisting of two inequalities joined by the word "and" we need to find all values of `x` that make both inequalities true. That is: he same `x` has to make both true.

Solving `4x+1 <= 17`, we get:
`4x <= 16`, so `x <= 4`

Solving `5x-1 > 19`, we get `x > 4`

To solve: "`4x+1 <= 17 " and "5x-1 > 19`", we need all `x`'s that solve

"`x <= 4 " and "x > 4`"

That is, we need an `x` that is, at the same time, both less than or equal to `4` and also strictly greater than `4`.

There is no such `x`, so the compound inequality has no solution.

(If you need to write the solution set, use the notation for the empty set: "`O/`")