Question

Inequality conjunctions

and disjunctions
Consider the inequality conjunction:
– 5 < x ≤ 7 .Draw the values of x given by – 5 < x ≤ 7 on a number line.

Answer 1

See pictures attached

Explanation:

The conjunction is given by the intersection of 2 inequalities

-5 < x (or x > -5)

that is the set of real number such that x greater than -5, graphically is represented by picture 1 attached (the parentheses means that -5 IS NOT included)

and the inequality

x ≤ 7

which is the set of real number such that x less than or equal to 7, represented in picture 2 attached (the bracket means that 7 IS included)

When we intersect the two sets we obtain

– 5 < x ≤ 7

that is the set of numbers x such that x is greater than -5 AND x less than or equals to 7, which graphically is represented in picture 3 attached.