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

1 Answer
Jul 7, 2015

Answer:

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/#")