Solving Simple Equations

Algebraic equations in single variable are called simple equations. For example, 2n+6=18; y-7=12; 12x+3= 15 etc.  While working on simple equations the following points are to be remembered:
The same thing has to be done on both sides of the equal to sign, this method is called balance
For instance, if we add 5 on left hand side then we must add the same number on the right hand side also.
Using of opposite operations to eliminate the terms is required.

This is a way to keep the balance in the equation. This is done by moving the terms around the equal to sign by using the opposite operation so as to undo the operation given in the equation.

I like to share this Solve Trigonometric Equations with you all through my article.

Operation opposite to addition is subtraction and vice versa
Operation opposite to multiplication is division and vice versa

For example, the opposite of product of 3 and x would be division by 3
Same variable having different coefficients are called like terms. For example, -5x, 3x are like terms. When an equation has like terms they are to be combined. 3x+12-5x-7x would be (3x-5x-7x)+ 12= -9x+12
If the terms are given in parenthesis in an equation those terms are to be simplified first and done using the distributive property. For example, 2(x-3)+7x+3 would be 2x-6+7x+3 =9x-3

While solving simple equations the order of steps to be followed are:
First step: eliminate any fractions in the equation
Second step: simplify the terms in the parenthesis
Third step: Combine all the like terms

Fourth step: Move all the terms around the equal to sign using the opposite operation method such that all the variable terms are on the left hand side and the numerical part on the left hand side (If addition operation then undo it by using subtraction operation and vice versa)

Fifth step: Isolate the variable using the opposite operation method and then simplify the numerical terms (if multiplication operation use the division operation to undo it and vice versa)

Solve the simple equation, -(1/2)x + 2(3+2x) = 13
Solution: First we need to eliminate the fraction and hence multiply throughout with 4
2(-1/2)x +2.2(3+2x) = 13.2   (balance)
-x+4(3+2x)= 26
Now applying the distributive property open the parenthesis
-x+12+8x = 26
Combining the like terms
-x+8x+12= 26
7x +12 = 26
Subtracting 12 on both sides to eliminate 12
7x+12-12 = 26 – 12
7x= 14
To undo the multiplication divide on both sides with 7
7x/7 = 14/7
Final answer, x=2
Checking: -(1/2)2+2[3+2(2)]=-1+14=13, LHS=RHS. Correct solution!

Algebra is widely used in day to day activities watch out for my forthcoming posts on help with factoring polynomials and cbse 11th sample paper. I am sure they will be helpful.