Introduction
 An equation is a mathematical statement that shows that two expressions are equal.
 Examples:, $2y=6$, $3m9=12$, etc.
 All the equations have an equal sign (=).
 An equation is said to be linear if it contains only one variable with the highest power of 1 (one).
Solving simple linear equations
 The value of the variable for which the equation is satisfied is called the solution of the equation.
 In order to solve an equation, perform the following steps as applicable:

 Combine like terms
 Solve using the addition principle
 Solve using the subtraction principle
 Solve using the multiplication principle
 Solve using the division principle
Solved Examples
Question 1: Solve the following equation.
$x+3=1$
Solution: $x+3=1$
Applying the subtraction rule.
$x+33=13$
$x=2$
Question 2: Solve the following equation.
$m2=5$
Solution: $m2=5$
Applying the addition rule.
$m2+2=5+2$
$m=7$
Question 3: Solve the following equation.
$\frac{x}{2}=4$
Solution: $\frac{x}{2}=4$
Apply the multiplication rule.
$\frac{x}{2}\times 2=4\times 2$
$x=8$
Question 4: Solve the following equation.
$7x=21$
Solution: $7x=21$
Apply the division rule.
$\frac{7x}{7}=\frac{21}{7}$
$x=3$
Cheat Sheet
 A mathematical statement that has two expressions separated by an equality sign is called an equation.
 An equation remains the same if its LHS and RHS are interchanged.
 The value of a variable for which the equation is satisfied is called the solution of the equation.
Blunder Areas
 Whatever operation you do on one side of the equation, perform the same operation on the other side as well.
 Pay close attention to the signs while performing any operation with negative numbers.
Solving simple linear inequalities (to be deleted)
 Inequalities can be solved using the rules mentioned below.

 Adding the same number to each side of an inequality produces an equivalent inequality wherein the sign of inequality remains unaffected.
 Subtracting the same number from both sides of an inequality results in an equivalent inequality wherein the sign of inequality remains unaffected.
 Multiplying both sides of an inequality by a positive number results in an equivalent inequality wherein the sign of inequality remains unaffected.
 Multiplying both sides of an inequality by a negative number results in a new inequality wherein the sign of inequality is reversed.
 Dividing both sides of an inequality by a positive number results in an equivalent inequality wherein the sign of inequality remains unaffected.
 Dividing both sides of an inequality by a negative number results in a new inequality wherein the sign of inequality is reversed.
 Abhishek Tiwari
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