In mathematics, linear inequality is one inequality that involves a linear function. Linear inequality has actually one that the icons of inequality. Reflects data the is not equal in the kind of a graph.
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Symbol of Inequality:
> higher than
≤ much less than or equal to
≥ higher than or same to
≠ not equal to
= same to
Linear Inequation of One Variable
Let a be the non-zero real number and also x be a variable. In one variable, inequalities that the type ax + b > 0, ax + b
Linear Inequation of two Variables
Let x, y be variables, and also a, b it is in non-zero actual numbers. The inequation the the form ax + by c, ax + by ≤ c, and ax + by ≥ c room then referred to as straight inequities in the two variables x and y.
Rules for fixing Inequalities
There are similar rules for addressing inequalities to those because that solving direct equations. However, once multiplying or dividing by a an unfavorable number, there is one exception. In order to fix inequalities, we can:
Add the very same number top top both sides.
From both sides, subtract the same number.
By the same optimistic number, main point both sides.
By the same positive number, division both sides.
Multiply the same an adverse number top top both sides and also reverse the sign.
Divide the same an adverse number in between both sides and reverse the sign.
Ex: solve x – 6 > 14
x – 6 > 14
x – 6+ 6 > 14 + 6
x > 20
Ex. Resolve the inequality 12 > 18 – y
12 > 18 – y
18 – y
18 – y – 18
y > 6
How to represent the equipment of a direct Inequality in One variable on a Number Line
We use the following conventions come depict the solution of a direct inequality in one change on a number line:
If the inequality involves ‘>’ or ‘
How come Graphically represent the equipment of a direct Inequality
1. To represent the solution of a linear inequality in a aircraft graphically in one or two variables, we continue as follows:
If the inequality requires ‘≥’ or ‘≤’, we attract the graph the the line together a thick heat to suggest that the point out on this line are consisted of in the systems set.
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If the inequality requires ‘>’ or ‘
2. Solution of a straight inequality in one variable have the right to be stood for on the number line and in the aircraft but the equipment of a straight inequality in two variables of the form ax + by > c, ax + by ≥ c, ax + by
3. A device of inequalities includes two or an ext inequalities take away together, and also the remedies to the mechanism of inequalities room the solutions typical to every the inequalities that form the system.