In mathematics, an inequality is regarded as the relation which is held between the two values when they are different. Equations and inequality are considered as the mathematical sentences that are formed by relating two expressions with each other. In equality the two expressions are not treated as necessarily equal that are represented by the symbols such as >, <, ≤ or ≥.
x>y – x is greater than y
x≥y – x is greater than or equal to y
It is noteworthy to denote that an equality comprises of a minimum of one variable which is known as open sentence. When an individual substitute the variable in the open sentence with the number leading to statement that are either true or false. If the statement is true, then the number is the solution to the equation or inequality.
If the values in the question are treated as the element of ordered set, namely the integers or the actual numbers, then they can be compared in size.
a.The symbolization a < b implies that a is less than b.
b.The representation a > b implies that a is greater than b.
In either of the cases a cannot be considered equal to b. These kind of relations is treated as strict inequalities. The representation that a < b might also be interpreted as a is strictly less than b.
The objective here is to have the X on its own on the left side of the inequality symbol
Something like: x < 5
Or; y ≥ 11
Example 1: Solved Example: x + 2 > 12
Subtracting 2 from each sides
X + 2 – 2 > 12 – 2
Simplifying it as;
X > 10
Example 2: Solved Example: 3x < 7 + 3
It can be simplified as 7 + 3 without impacting the inequality:
3x < 10
Example: 2y + 7 < 12
When swapping the left and right side, one should also change the direction of the inequality as well:
12 > 2y + 7
Example 3: Solved Example: 12 < x + 5
Upon subtracting 5 from both the sides, it is understood that;
12 – 5 < x + 5 – 5
7 < x
That is the solution!
Solved Example 4: Example: Can 4 be the solution to
4a – 5 < 3 + 3a
Now substituting a for 4
4 x 4 – 5 < 3 + 3 x 4
16 – 5 < 3 + 12
11 < 15
True! 4 is the solution to inequality.
Solved Example 5: Example:
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