# Linear equations in one unknown

An equation of the shape:
*
ax
+
b
*
= 0,
*
*
where
*
a
*
and
*
b
*
– the known numbers,
*
x
*
– an unknown
value, is called a
**
linear equation in one unknown.
**
To solve this
equation means to find the numerical value of

*x*, at which this equation becomes an identity.

If
*
a
*
is not equal to zero (
*
a
*
≠
0
), then a solution ( root ) has the shape:

*
*

If
*
a
*
= 0 , then
the
*
*
two
cases are possible:

*
*

1
*
.
*
*
b
*
= 0,
*
*
then
0
·
*
x
*
+ 0 = 0
*
.
*
Here
*
x
*
can be
*
any
number
*
( check this ! ).

2
*
.
*
*
b
*
≠ 0,
*
*
then
0
·
*
x
*
+
*
b
*
= 0
*
.
*
*
There is no solution
*
( check this also ).

expressions:
*
x
*
^{
2
}
*
+
*
2
*
x = x
*
^{
2
}
*
–
*
2
*
x
+ x –
*
2
*
*
.
*
*
Transfer all terms to the

left-hand side of the equation. After reducing all similar terms we’ll

receive:
3
*
x
*
+ 2 = 0,
*
*
hence
*
x = –
*
2 / 3
*
*
.