equations & inequalities furqan m lodhi

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Equations & Inequalities

Equation

Equation are the basic mathematical tool for solving real-world problem

To solve the problem, we must know how to construct equation that model real-life situations.

equation

Linear Equation

Quadratic Equation Polynomial equation

equation

Linear Equation

Simultaneous Equation for 2 x

2 system

Quadratic Equation

Addition and subtraction

Factorization

Completing the square

Formulae

Substitution

Elimination

Linear equationsAddition and subtraction

Multiplication and division

Quadratic EquationFactorization Formulae

Completing the square

If a = 1

Solving of quadratic equation

• By factoring1. Solve the equation Solution:

By completing the square2. Solve the equation Solution:

Simultaneous equation

• Simultaneous equation has two or more equation that has similar set of solution. Linear equation can be solved by using substitution and elimination method.

Simultaneous Equation for 2

x 2 systemSubstitution Elimination

example

inequalities• An inequality says that two values are not equal.

a ≠ b says that a is not equal to b

There are other special symbols that show in what way things are not equal.

a < b says that a is less than ba > b says that a is greater than b(those two are known as strict inequality)

a ≤ b means that a is less than or equal to ba ≥ b means that a is greater than or equal to b.

inequality

Inequalities

Absolute value

Linear Inequality

Quadratic Inequality

Inequalities

Linear Inequality Quadratic Inequality

Single Inequality Double Inequality

Absolute value

, 0

, 0

x if xx

x if x

• Properties of absolute value

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• Absolute value equations

or x = -a with a is real number positive

axax

Example :

Inequality

• Linear inequality with one variable

THE ENDPlease Do a Lot of Exercises

JUST REMEMBER:

MATHS IS FUN