Question

If the replacement set = {-7,-5,-3,-1,0,1,3}, find the solution set of
(i) $x > - 2$
(ii) $x < - 2$
(iii) $x > 2$

Answer 1

Hint: To solve this question, we need to know the basic theory related to the set theory. As we know, the essential features of set theory is making sets involve the grouping of objects of any kind into a single entity. Here, we will simply use given inequality and know the solution set as discussed below.

Complete step-by-step answer:
As we know, finding a solution set to an inequality, given a replacement set, is similar to finding a solution set to an equation.
(i) $x > - 2$
The given inequality is $x > - 2$.
And the replacement set = {-7,-5,-3,-1,0,1,3}.
Here, by observing we concluded that -1, 0, 1 and 3 are greater than -2. So, we say it will satisfy the given inequality $x > - 2$.
Therefore, the solution set is {-1,0,1,3}.
(ii) $x < - 2$
The given inequality is $x < - 2$.
And the replacement set = {-7,-5,-3,-1,0,1,3}.
Here, by observing we concluded that -7, -5 and -3 are less than -2. So, we say it will satisfy the given inequality $x < - 2$.
Therefore, the solution set is {-7,-5,-3}.
(iii) $x > 2$
The given inequality is $x > 2$.
And the replacement set = {-7,-5,-3,-1,0,1,3}.
Here, by observing we concluded that 3 are greater than 2. So, we say it will satisfy the given inequality $x > 2$.
Therefore, the solution set is {3}.

Note: In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities. For example, for a set of polynomials over a ring, the solution set is the subset on which the polynomials all vanish (evaluate to 0).