There, we gave introduction to equations and explained various terms such as Open Sentence, Equation, Solution or Root(s) of an Equation, Domain of the variable and Kinds of Equations.
That knowledge is a prerequisite here.
Here, we deal with equations in which the highest exponent of the varaible(s) present is one.
We explain the method of solving the equations with a number of solved examples.
Several problems are given for practice in exercise with answers.
Practice makes one perfect.
This is especially true for learning of solving Algebra Problems (Math Problems).
So, take the exercises seriously and practice solving the problems.
Linear Equations in one variable
The general form of this is ax + b = 0, where a, b are real numbers (a ≠ 0). These are also called Simple Equations.
Solving Simple Equations :
We know that solving an equation means
finding the replacement value(s) of the variable for which the L.H.S.and R.H.S. of the equation become equal.
We can observe
if the same number is added (or subtracted) to both sidesof an equality, the equality is not altered.
Example 1
Solve the Equation x - 5 = 10.
Solution: The given equation is x -5 = 10 Adding 5 to both sides, we get x -5 + 5 = 10 + 5 ⇒ x = 15. Ans.
Example 2
Solve the Equation x + 9 = 4.
Solution: The given equation is x + 9 = 4 Subtracting 9 from both sides, we get x + 9 - 9 = 4 - 9 ⇒ x = -5. Ans.
We can aslo see
if both sides of an equality are multiplied (or divided) by a non zero number, the equality is not altered.
Example 3
Solve the Equation p⁄3 = 5.
Solution: The given equation is p⁄3 = 5 Multiplying both sides by 3, we get (p⁄3) x 3 = 5 x 3 ⇒ p = 15. Ans.
Example 4
Solve the Equation 5y = -20.
Solution: The given equation is 5y = -20 Dividing both sides by 5, we get 5y⁄5 = -20⁄5 ⇒ y = -4. Ans.
Transposition in Linear Equations
For studying Solving Equations by the method of Transposition, go to
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