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# Linear Inequalities

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A linear inequality is the combination of variable, constant and operation with inequality sign > (greater than), < (lesser than), $\geq$ (greater than or equal to) and $\leqslant$ (lesser than or equal to) where the highest power of the variable is one i.e. a linear inequality always has a degree one. For example: x + 3 > 4 is an example of linear inequality
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Linear Inequalities
A linear inequality is the combination of variable, constant and operation with inequality sign > (greater
than), < (lesser than), $\geq$ (greater than or equal to) and $\leqslant$ (lesser than or equal to) where the
highest power of the variable is one i.e. a linear inequality always has a degree one.
For example: x + 3 > 4 is an example of linear inequality

Properties of Linear inequalities
* Subtraction property : If you subtract same number from each side of
inequality the inequality still holds. If a < b than a - c < b - c. Similarly for
other inequality signs.
* Addition property :If you add same number to each side of the inequality,
the inequality stil holds. If a< b than a + b < b + c. Similarly for other
inequality signs.
* Multiplication property : If you multiply each side of the inequality by a
positive number the direction of inequality remains unchanged.But if you
multiply each side of the inequality by a negative number the direction of
inequality sign changes. If a < b than a * c < b * c. However, if a < b than a * (-
c ) > b * (-c). Similarly for other inequality signs.
* Division property: If you divide each side of the inequality by a positive
number the direction of the inequality remains unchanged but if you divide
each side of the inequality by a negative number than the direction of the
inequality get changed. If a < b than $\frac{a}{b}$ < $\frac{b}{c}$ . however, if
$\frac{a}{-c}$ < $\frac{b}{-c}$ , we get $\frac{a}{-c}$ > $\frac{b}{-c}$

R
ead More on graphing linear inequalities

Practice Problems
Problem 1: Solve the inequality: 21 > - 3m. Find the value of x for which the inequality holds.Graph the inequality
in a number line.( Ans : m > - 7)
Problem 2: Solve the inequality: x - 5 $\geq$ 6. Find the value or values of x for which the inequality holds. Graph
the inequality in a number line. ( Ans: x $\geq$ 11)

Thank You
TutorVista.com

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Linear Inequalities

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