Question

Solve the compound inequality.

4−5x≤3<4

a) The solution set is
(−[infinity], 1/5 ]
b) The solution set is ∅
c) The solution set is (−[infinity],1)
d) The solution set is (−[infinity],0.2]

Answer 1

To solve the compound inequality 4 - 5x ≤ 3 < 4, break it down into two separate inequalities and find the solution for each one. The solution set for the compound inequality is (−∞, 1/5].

Step-by-step explanation:

To solve the compound inequality 4 - 5x ≤ 3 < 4, we need to break it down into two separate inequalities and find the solution for each one:

1. First inequality: 4 - 5x ≤ 3. Subtract 4 from both sides to get -5x ≤ -1. Then divide both sides by -5, remembering to reverse the inequality sign since we're dividing by a negative number. This gives us x ≥ 1/5.
2. Second inequality: 3 < 4. This is a simple inequality with no variables. Since 3 is less than 4, it's always true. So there is no restriction on x for this inequality.

To find the solution set for the compound inequality, we need to find the overlapping region between the two inequalities. Since there is no restriction on x for the second inequality, the overlapping region is x ≥ 1/5. Therefore, the correct solution set for the compound inequality is (−∞, 1/5].