Solve: 3x+8 > 2, when - x is an integer.
- x is a real number.
- x is an integer.
- x is a real number.
Solution and Explanation
The given inequality is 3x+8 > 2.
3x-8 > 2
⇒ 3x-8-8 > 2-8
⇒ 3x > -6
⇒ \(\frac {3x}{3}\) > \(-\frac {6}{3}\)
⇒ x > -2
(i) The integers greater than –2 are –1, 0, 1, 2, …
Thus, when x is an integer, the solutions of the given inequality are –1, 0, 1, 2 …
Hence, in this case, the solution set is {–1, 0, 1, 2, …}.
(ii) When x is a real number, the solutions of the given inequality are all the real numbers, which are greater than –2.
Thus, in this case, the solution set is (– 2, ∞).
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Concepts Used:
Inequalities
In mathematics, inequality is a relationship that compares two numbers or other mathematical expressions in a non-equal fashion. It is most commonly used to compare the size of two numbers on a number line.
Specifically, a linear inequality is a mathematical inequality that integrates a linear function. One of the symbols of inequality is observed in a linear inequality: In graph form, it represents data that is not equal.
Some of the linear inequality symbols are given below:
- < less than
- > greater than
- ≤ less than or equal to
- ≥ greater than or equal to
- ≠ not equal to
- = equal to
Inequalities can be demonstrated as questions that are solved using alike procedures to equations, or as statements of fact in the form of theorems. It is used to contrast numbers and find the range or ranges of values that pleases a variable's criteria.