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LINEAR EQUATIONS

A linear equation can be defined as an equation in which the highest exponent of the equation variable

is one. When graphed, the equation is shown as a single line.

+

2 =

← Linear equation: highest exponent of the variable is 1.

Example:

x

4

A linear equation has only one solution. The solution of a linear equation is equal to the value of the

unknown variable that makes the linear equation true.

+

2 =

← The value of the unknown variable that makes the equation

Example:

x

4

=

4 −

+

=

x

2

true is 2:

2

2

4

=

x

2

There are different forms of writing a linear equation. Each form has a different way of solving the linear

equation that makes the process easier. There is only one rule that applies to any form of linear equations:

whatever you do on one side you need to do on the other side. That is, if you add on the left side, you

need to add on the right side. If you multiply on the left side, you need to multiply on the right side, and

so on.

+

=

−

=

1. Equations of the form

x

a

b

or

x

a

b

.

Linear equations in this form are solved by adding or subtracting the same quantity to both sides with

the idea of leaving the variable by itself. That is, isolating the variable.

−

5 =

x

10

Examples:

← Add 5 to both sides to eliminate the number

−

+

=

+

x

5

5

10

5

On the left side of the equation and leave x alone.

=

x

15

+

3 =

y

2 .

4

1 .

← Subtract 3.2 to both sides to eliminate the

+

−

=

−

y

3

2 .

3

2 .

4

1 .

3

2 .

=

number on the left side and isolate y.

y

0

9 .

ax = .

2. Equations of the form

b

Linear equations in the form of multiplication are solved by dividing both sides of the equation by the

number multiplying the variable. When a fraction is multiplying the variable, multiply both sides of

the equation by the reciprocal of the fraction attached to the variable.

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Parent category: Education