Question

Solve x>0 and x>-5 and write the solution in interval notation. If there is no solution,type Ø.

a) (−5,0)
b) (0,[infinity])
c) Ø
d) (-[infinity], [infinity])

Answer 1

The solution to the inequalities x > 0 and x > -5 is any number greater than 0. In interval notation, this is represented as (0, infinity), option b).

Step-by-step explanation:

To solve the inequalities x > 0 and x > -5, we need to find the set of values that satisfy both conditions at the same time. Since the first condition, x > 0, is stricter than the second, x > -5, the solution will be determined by the first condition alone. Any value that is greater than zero will automatically be greater than -5.

Therefore, the solution to both inequalities is the set of all numbers greater than 0. In interval notation, this is represented as (0, ∞), which corresponds to option b).