Benjamin T. answered • 09/03/22
Physics Professor, and Former Math Department Head
Both inequalities have one dimension (just x) so you can solve them independently and combine them. With some algebra,
2x-7≤1 ⇒ x≤4
2x+1>3 ⇒ x>1
In interval notation the solution sets become (-∞, 4] and (1,∞). They do overlap so you need to consider the overlap when you combine both intervals, giving the solution (-∞,∞).
To do a brief check on the solution, if a number is less than or equal to 1 (consider 0) only the first inequality is true. If a number if greater than one and less than or equal to 4 (consider 2) both in equalities are true. If a number is greater than 4 (consider 5) only the second inequality is true. That includes all real numbers.
