We may verify this result; each side of the equation will be

Verification; put this value for x in the original equation;

166. We may remark that an equation of the first degree cannot have more than one root. For any equation of the first degree will take the form ax=b if the unknown quantity is brought to one side of the equation, and the known quantities to b the other, and to make this true x must be equal to and to nothing else.

α

The result is sometimes obtained thus. Suppose, if possible, that this equation has two different roots a and ẞ; then by supposition,

but this is impossible, since by supposition a-ẞ'is not zero, and a is not zero. Thus an equation of the first degree cannot have

more than one root.

7 11

1

+

х

Ꮳ

+5=x

3

2

2

3

=

x + 3

х

5

6

77

x + 4

36. (x-5) (x-2)-(x-5) (2x-5)+(x+7) (x − 2) = 0.

37.

3-x-2(x-1)(x + 2) = (x − 3) (5 – 2x).

(27 72 + 1).

+1.

38. x-3-(3-x) (x + 1) = (x-3) (1+x) + 3-x.