Algebraic Equation Linear Equation In One Variable Equations Reducible To Simpler Form Solving Linear Equation In One Variable Linear Equations in One Variable An algebraic equation with only one type of variable. Equations of type = are not linear equations but can be reduced by cross-multiplication These type of equations can be solved by either of the two methods mentioned earlier. = 4 — 4 4x — 4 ² 4x + 5 = 9 ; write the equation ² 4x + 5 - 5 = 9 - 5 ; Subtracting 5 on both sides, hence not disturbing the balance. ² 4x = 4 ; Simplifying ² x = 1 ; Simplifying ; Dividing by 4 on both sides,hence not disturbing the balance Type 1 : Variable on one side and number on the other side. For e.g. 4x + 5 = 9 In this method the numbers are moved from one side of equality to other side by changing the sign. The changes are as follows, Balancing Method 1 2 3 It is an equality involving variables For e.g. The value of the variable which satisfies the equation is its solution 4x + 5 = 3x - 2 Left Hand Side(LHS) Right Hand Side(RHS) Equality 1 + changes to - - changes to + % changes to ' ' changes to % i ii iii iv a a The rules of transposing numbers are also applicable for variables b Transposing Method b Type 2 : Variables and numbers on both sides. For e.g. 2x - 3 = x + 2 2 For e.g. 4x + 5 = 9 Taking 5 to RHS 4x = 9 - 5 4x = 4 Taking 4 to RHS x = 4 — 4 x = 1 For e.g. 2x - 3 = x + 2 Taking 3 to RHS 2x = x + 2 + 3 2x = x + 5 Taking x to LHS 2x - x = 5 x = 5 2( 4x + 3 ) = 3( 3x + 7 ) 8x + 6 = 9x + 21 And this can be further sorted by transposition 8x = 9x + 21 - 6 8x = 9x +15 -15 = 9x - 8x x = -15 4x + 3 3x + 7 3 — 2 4x + 3 3x + 7 3 — 2
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Algebraic Equation
Linear Equation In One Variable
Equations Reducible To Simpler Form
Solving Linear Equation In One Variable
Linear Equations in One Variable
An algebraic equation with only one type of variable.
Equations of type =
are not linear equations but can be reduced by cross-multiplication
These type of equations can be solved by either of the two methods mentionedearlier.
= 4—44x—4
² 4x + 5 = 9 ; write the equation
² 4x + 5 - 5 = 9 - 5 ; Subtracting 5 on both sides, hence not disturbing the balance.² 4x = 4 ; Simplifying
² x = 1 ; Simplifying
; Dividing by 4 on both sides,hence not disturbing the balance
Type 1 : Variable on one side and number on the other side. For e.g. 4x + 5 = 9
In this method the numbers are moved from one side of equality to other sideby changing the sign. The changes are as follows,
Balancing Method
1
2
3
It is an equality involving variablesFor e.g.
The value of the variable which satis�es the equation is its solution
4x + 5 = 3x - 2
Left Hand Side(LHS) Right Hand Side(RHS)Equality
1
+ changes to -- changes to +% changes to '' changes to %
i
ii
iii
iv
a
a
The rules of transposing numbers are also applicable for variablesb
Transposing Methodb
Type 2 : Variables and numbers on both sides. For e.g. 2x - 3 = x + 22
For e.g.4x + 5 = 9
Taking 5 to RHS4x = 9 - 5
4x = 4Taking 4 to RHS
x = 4—4x = 1
For e.g.2x - 3 = x + 2
Taking 3 to RHS2x = x + 2 + 3
2x = x + 5Taking x to LHS
2x - x = 5x = 5
2( 4x + 3 ) = 3( 3x + 7 )8x + 6 = 9x + 21
And this can be further sorted by transposition
8x = 9x + 21 - 6 8x = 9x +15-15 = 9x - 8x
x = -15
4x + 33x + 7
3—2
4x + 33x + 7
3—2
Related Documents
