Introduction
 An expression is a mathematical statement made up of numbers, variables, and arithmetic operators (such as addition and subtraction).
 Consider the example shown below to understand the different components of an expression.
 Notice that an expression does not contain an equal sign or inequality symbol.
 The expressions that contain a variable are called algebraic expressions.
 The terms with the same variable(s) raised to the same exponent are called "like terms."
 Expressions and equations are not the same.
 An equation consists of two expressions separated by an equal sign.
 For example, $4x+8=2x1$ is an equation.
Difference between Expressions and Equations
 The main difference between an expression and an equation is that expressions don't equate to anything, whereas an equation does.
 Expressions are used to create equations.
Simplifying Expressions
 An algebraic expression is simplified in order to get a condensed equivalent algebraic expression.
 In order to simplify an algebraic expression, perform the following steps as applicable:

 Express the given expression in expanded form, if possible.
 Identify like terms.
 Combine like terms to get a simplified expression.
 Note: Obey the order of operation when combining like terms.
Solving Equations
 In order to solve an equation, perform the following steps as applicable:

 Remove parenthesis
 Combine like terms
 Apply distributive property
 Solve using the division principle
 Solve using the multiplication principle
 Solve using the addition principle
 Solve using the subtraction principle
Solved Examples
Question 1: Simplify the expression: $2x+10\left(x\right)+2$
Solution: $2x+10\left(x\right)+2$
Remove parenthesis:
$=2x+10+x+2$
Combining like terms:
$=3x+12$
Question 2: Solve the equation: $4x3=2x+1$.
Solution: $4x3=2x+1$
Subtraction principle:
$4x32x=2x+12x$
$2x3=1$
Addition principle:
$2x3+3=1+3$
$2x=4$
Division principle:
$\frac{2}{2}x=\frac{4}{2}$
$x=2$
Question 3: Solve the equation: $2\left(13x\right)+13=3\left(x1\right)$.
Solution: $2\left(13x\right)+13=3\left(x1\right)$
Remove parenthesis:
$26x+13=3x3$
Subtraction principle:
$26x+133x=3x33x$
$159x=3$
Subtraction principle:
$159x15=315$
$9x=18$
Division principle:
$\frac{9}{9}x=\frac{18}{9}$
$x=2$
Cheat Sheet
 To simplify an expression, we first express it in expanded form (get rid of parenthesis), identify and combine the like terms to get an expression in a compact form.
 To solve an equation, perform the following steps as applicable:

 Remove parenthesis
 Combine like terms
 Apply distributive property
 Solve using the division principle
 Solve using the multiplication principle
 Solve using the addition principle
 Solve using the subtraction principle
Blunder Areas
 Remember that addition and subtraction operations can only be performed on like terms.
 Abhishek Tiwari
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