LINEAR EQUATIONS - SOLVING, SOLVED EXAMPLES AND EXERCISE, LINKS TO WORD PROBLEMS

Please study
Math Equations before Linear Equations,
if you have not already done so.

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 sides of 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

Solving Equations by Transposition.

Linear Equations with fractional and decimal coefficients

For studying Solving Equations with
fractional and decimal coefficients, go to

Solving Equations with fractional and decimal coefficients

Word Problems

For Word Problems on Equations in one Variable, go to

Algebra Word Problems.

For Equations in two Variables
including Word problems, go to

Equations in Two Variables

Exercise :

1. Solve the equation
   x + 5 = 7
2. Solve the equation
   27 = 3x
3. Solve the equation
   x⁄7 = -8

Answers to Exercise :

1. 2
2. 9
3. -56