SIMPLE EQUATIONS. 333 



SIMPLE EQUATIONS. 



An Equation is when two equal quantities, difFerently 

 expressed, are compared together by means of the sign 

 = placed between them. ^ 



Thus, 1 2 — '5=7 ii an equation, expressing the et^uaKty 

 of the quantities 12— ?-5 and 7. 



A simple equation is that, which contains only One un«s 

 known quantity, in its simple form, or not raised to any 

 power. 



Thus, a;— fl-^^zr^ is a simple equation, containing on-e 

 \j the unknown quantity x, 



"Reduction of equations is the method of finding the valu^ 

 of the unknown quantity. It consists in ordering the 

 equation so, that the unknown quantity may stand alone 

 on one side of the equation without a coefficient, and all 

 the rest, or the known quantities, on the other side. 



RULE I,* 



Any quantity may be transposed from one side of the 

 equ^,tion to the other, by changing its sign. 



Thus, if flf-|-3=7, then will iv::=7 — 33=4. 



And, if ;vr— 4+6~z8, then will ;tf=:8+4— 6z=6. 



Also, if ii—^a-^fhzzc-^dy then will ;vZZr— -^-{-^ — h* 



And, in like manner, if 4^---8z;3:v-|-2o, then will 43? 

 f--3iv=;:2o-j-8, or ;v:;:;28. 



RULE 



* These are founded on the general princ^le of performing 

 equal operations on equal quantities, when it is evident, that the 

 results must still be equal ; whether by equal additions, or sub-, 

 tractions, or multiplications, or divisions, or roots, or powers. 



