5x + 3 ≤ -2 or 13 – x ≤ 6

Question

Show the solution sets written algebraically and as a union or intersection of intervals.  then display a simple line graph for each solution set

Answer 1

5x+3≤-2, 5x≤-5, x≤-1, x∈(-∞,-1] ; 13-x≤6, 7≤x, x≥7, x∈[7,∞).

Let set A={ all x | x≤-1 }, set B={ all x | x≥7 }.

A⋃B is the set of all solutions satisfying the given inequalities. The red lines (each extended indefinitely to -∞ or ∞) represent the solution set, with the endpoints -1 and 7 shown. The zero point is shown for reference only (not part of the set).