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: The replacement set is the set of values that may be substituted for the variable. To find the solution set from the replacement set, plug in each value from the replacement set and evaluate both sides of the equation. If the two sides are equal, the equation is true and thus the value is a solution

Complete step-by-step answer:
Given
The replacement set = {-7, -5, -3, -1, 0, 1, 3}, the set contains 7 numbers to it
Now we will find the set of the numbers which will lie in the given set for the following given conditions one by one, for
\[x > - 1\]
Now we will find the set of the numbers which are greater than -1 from the given replacement set of numbers, hence we can write
\[x > - 1 = \left\{ {0,1,3} \right\}\]

\[x < - 2\]
Now we will find the set of the numbers which are smaller than -2 from the given replacement set of numbers, hence we can write
\[x < - 2 = \left\{ { - 3, - 5, - 7} \right\}\]

\[x > 2\]
Now we will find the set of the numbers which are greater than 2 from the given replacement set of numbers, hence we can write
\[x > - 1 = \left\{ {0,1,3} \right\}\]
Hence we get all the sets for the following given condition.

Note: The set from which the values of the variable which are involved in an in-equation are chosen is known as the replacement set. Students must note that while finding the solution set of numbers from the given replacement set they must carefully understand the given condition for which the solution set is being formed.