Definitions and notations

Linear Equations:

Equations in which the exponent(Power) of a variable of the equation is 1 are called linear Equations. Such as $ax+b=c$ where a , b and c are constant and x is the variable with power 1.

Coefficient:

The number in front of the variable is coefficient such as $ax+b=c$, here a is the coefficient of x

Rational Coefficient:

If the coefficient of variable is a rational number then it is called a rational coefficient.

Radical Expression:

An expression that contains any kind of root is called a radical expression such as $\sqrt{3x+2}+7$ is a radical expression.

Radical Equation:

Any equation that contains radical expression are called radical equations such as $\sqrt{3x+2}+7=8$

Absolute Value:

Absolute value is the distance of a real number from 0 either from left or right of zero. It is denoted as $|x|$ where x is the real number. It is defined as

$|x|=\{\begin{array}{} \ & \begin{array}{} x, & \text{when \space\space}x> 0 \\ 0, & \text{when \space\space}x = 0\\ -x & \text{when \space\space} x<0 \end{array} \end{array}$

For example $|-5|=5,|+7|=7$

$\fbox{Note: The absolute value of a number is always positive.}$

Less than “<”:

Less than sign denotes all values that are less than the given number. For example x<3 can be seen in the number line below.

Greater than “>”:

Greater than sign denotes all values that are greater than the given number. For example x>-3 can be seen in the number line below.

Less than or equal to$“\leq”$:

Less than or equal sign denotes all values that are less than the given number including the number it self as well. For example $x\leq4$ can be seen in the number line below.

Greater than or equal to$“\geq”$:

Greater than sign denotes all values that are greater than the given number including the number it self as well. For example $x\geq-2$ can be seen in the number line below.

$\fbox{Note : “Hollow" circle on number lines shows that number is not included and “Dark" circle shows that number is included }$