LINEAR EQUATIONS - SOLVING, SOLVED EXAMPLES AND EXERCISE, LINKS TO WORD PROBLEMS
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
a + x = 0, b where , a are real numbers ( b ≠ 0). a 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
- 5 = 10. x
The given equation is -5 = 10 x Adding 5 to both sides, we get -5 + 5 = 10 + 5 ⇒ x = 15. Ans.
x Example 2
Solve the Equation
+ 9 = 4. x
The given equation is + 9 = 4 x Subtracting 9 from both sides, we get + 9 - 9 = 4 - 9 ⇒ x = -5. Ans. x
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
⁄3 = 5. p
The given equation is ⁄3 = 5 p Multiplying both sides by 3, we get ( ⁄3) x 3 = 5 x 3 ⇒ p = 15. Ans.
p Example 4
Solve the Equation 5
= -20. y
The given equation is 5 = -20 y Dividing both sides by 5, we get 5 ⁄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.
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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
Great Deals on School & Homeschool Curriculum Books
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
Solve the equation + 5 = 7 x Solve the equation 27 = 3 x Solve the equation ⁄7 = -8 x Progressive Learning of Math : Linear equations
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Answers to Exercise : Linear equations
2 9 -56