The matching between the given inequalities and their solutions is as follows:
i) x ≥ 7.8; solution set is [7.8, ∞)
ii) x < 7.8; solution set is (-∞, 7.8)
iii) x ≤ 7.8; solution set is (-∞, 7.8]
iv) x > 7.8; solution set is (7.8, ∞)
What are the steps to write a solution set for an inequality?
Step 1: Solve the inequality for the values which makes it a true statement.
Step 2: Check the inequality symbol used.
- If it is 'less than or 'greater than then the obtained value is excluded from the set and represented in between open brackets. I..e, (a, b)
- If it is 'less than or equal to or 'greater than or equal to' then the obtained value is included in the set and represented in between square brackets. I..e, [a, b]
Writing the solution sets:
i) x ≥ 7.8
Since it is 'greater than or equal to the symbol (≥), the starting value is 7.8 which is included in the set and the end value is ∞. So, the solution set as
x: x ∈ [7.8, ∞)
ii) x < 7.8
Since it is 'less than symbol (<), the starting value is -∞ and the end value is 7.8 which is excluded from the set. So, the solution set as
x: x ∈ (-∞, 7.8)
iii) x ≤ 7.8
Since it is 'less than or equal to the symbol (≤), the starting value is -∞ and the end value is 7.8 which is included in the set. So, the solution set as
x: x ∈ [-∞, 7.8)
iv) x > 7.8
Since it is 'greater than symbol (>), the starting value is 7.8 which is excluded from the set and the end value is ∞. So, the solution set as
x: x ∈ (7.8, ∞)
Thus, the solution sets for all the given inequalities are matched with the respective inequalities.
Learn more about the solution set of inequality here:
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