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Linear Equations in One Variable

    Introduction

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8th class > Linear Equations in One Variable > Introduction

Introduction

Click on instructions button for directions on how to use the component and solve the given problems.

In the earlier classes, you have come across several algebraic expressions and equations. Some examples of expressions we have so far worked with are:

5x, 2x−3, 3x+y, 2xy+5, xyz+x+y+z, x2+1, y+y2

Some examples of equations are: 5x=25, 2x−3=9,2y+52 = 372 , 6z+10 = −2

You would remember that equations use the equality (=) sign; it is missing in expressions.

Of these given expressions, many have more than one variable. For example, 2xy + 5 has variables.

We however, restrict to expressions with only one variable when we form equations. Moreover, the expressions we use to form equations are linear. This means that the highest power of the variable appearing in the expression is .

These are linear expressions:

2x, 2x + 1, 3y – 7, 12 – 5z, 54 (x-4) + 10

These are not linear expressions:

x2 + 1 , y+y2, 1 + z + z2 + z3 (since highest power of variable > 1)

Here we will deal with equations with linear expressions in one variable only. Such equations are known as linear equations in one variable. The simple equations which you studied in the earlier classes were all of this type.

Let us briefly revise what we know:

(a) An algebraic equation is an equality involving variables. It has an equality sign. The expression on the left of the equality sign is the Left Hand Side (LHS). The expression on the right of the equality sign is the Right Hand Side (RHS).

(b) In an equation the values of the expressions on the LHS and RHS are . This happens to be true only for certain values of the variable. These values are the of the equation.

Instructions

Taking: 2x – 3 = 7, we have that x = 5 is the solution of the equation.
But what does it mean ?
For x = 5: LHS = 2 × 5 – 3 = which is to RHS that is 7.
For x = 10 : LHS = 2 × 10 – 3 = . This is to the RHS that is 7.
Thus, x = 5 is a solution while x = 10 is not a solution of the equation.

(c) How to find the solution of an equation? We assume that the two sides of the equation are balanced. We perform the same mathematical operations on both sides of the equation, so that the balance is not disturbed. A few such steps give the solution.