[color=#0000ff]Equation means equality for two expressions.[/color] An equation is [color=#0000ff]equivalent with the  original equation, if[/color] [br][list][*][color=#0000ff]the same number is added[/color] for both sides of the equation,[/*][br][*]the same number is [color=#0000ff]subtracted[/color] from both sides of the equation,[/*][br][*]both sides are [color=#0000ff]multiplied or divided[/color] with the same number which is [color=#0000ff]NOT zero[/color].[/*][/list][br][br]

[size=100][color=#0000ff][size=150][b]Standard form:[/b][/size][/color][/size][br]  [br]  [math]\LARGE\textcolor{blue}{ax+b=0\;\;\;a,b\in \cal R,\;a\neq 0}[/math][br][br]where [i]x [/i]is the variable and [i]a[/i] and [i]b[/i] are parameters (values unknown but constant). The solution (the root of equation) is [br]   [math]\LARGE\textcolor{blue}{x=-\frac{b}{a},}[/math][br] [br]where [math]\Large a \neq 0[/math] . If [i]a[/i] = 0 and [i]b[/i] = 0, then any value of satisfies the equation (identically true).[br]If [i]a[/i] = 0 and , the equation has no root (identically false).[br]  [br]Solving linear equations [br][list=1][*]Remove all brackets and denominators.[/*][br][*]Transpose the equation so that terms with variable are in one side of the equation and constants are on the other side.[/*][br][*]Combine like terms for to get the equation into a form ax = b.[/*][br][*]Divide by the multiplier of the variable.[/*][br][*]Check the root by substituting it to the original equation.[/*][/list]