The inequality 4x + 7 ≠ 23 can be rewritten as 4x ≠ 16 or x ≠ 4. Therefore, any set of numbers that does not include 4 or any number that would make 4x = 16 (i.e. x = 4) will contain only solutions to the inequality.
a) {1, 2, 3, 5} - This set only contains numbers that are less than 4, so they are all solutions.
b) {0, 4, 8, 12} - This set contains 4, which is not a solution.
c) {4, 5, 6, 7} - This set contains 4, which is not a solution.
d) {3, 3.5, 4, 4.5} - This set contains 4 and also includes numbers that would make 4x = 16 (i.e. x = 4), so only 3 and 3.5 are solutions.
Therefore, the set of numbers where all the numbers are solutions of 4x + 7 ≠ 23 is {1, 2, 3, 5}.
In which of the given sets of numbers are all the numbers solutions of 4x + 7 ≠ 23?
1 answer