...multiplied, or divided, by the same number, without destroying the equality. 72. Transposition of Terms. A term may be transposed from one member of an equation to the other by changing its sign. Let the equation be x + a — b. Subtracting a from both members (§ 71, 1),...

...are divided by equals, the quotients are equal. 6. Equal powers of equal quantities are equal. 49. PRINCIPLE. A term may be transposed from one member of an equation to the other if its sign is changed from + to — , or from — to +. EQUATIONS AND PROBLEMS. 50. 1. Given 2x —...

...multiplied, or divided, by the same number, without destroying the equality. 72. Transposition of Terms. A term may be transposed from one member of an equation to the other by changing its sign. Let the equation be x + a = b. Subtracting a from both members (§ 71, 1), we...

...onn member to the other, the sign of the quantity is changed ; hence the following rule. , Role. — A term may be transposed from one member of an equation to the other, if, at the same time, the sign be changed. EXAMPLES. In the following examples transpose the known...

...equality ? 13. What, then, may be done to the members of an equation without destroying the equality ? 70. The parts of an equation on each side of the sign...AXIOMS. — 1. Things that are equal to the same thing arc equal to each other. 2. If equals are ad/led to equals, the sums are equal. 3. If equals are subtracted...

...member. Example: ? + x = I*. Subtract 7 from both members. * = 12 — 7, or x = 5. It will be seen that a term may be transposed from one member of an equation to the other by changing its sign from + to — , or from — to +. The following rules are, therefore, obtained...

...of the equation to the other, and its sign has been changed from + to —. 52. Principle.—A number may be transposed from one member of an equation to the other by changing its sign from + to —, or from — to +. Solution of the Equation 53. If in any equation...

...disappeared from the second member, and appeared in the first, with a different sign before it. 39. Any term may be transposed from one member of an equation to the other by dropping it from the member in which it stands, and writing it in the other, with a different sign....

...12 + 3. Uniting like terms, (3) 3 x = 15, (4) x — 5. Axiom 5. From this solution it appears that a term may be transposed from one member of an equation to the other member by changing its sign. This process is called transposition. Accordingly, the above solution...

...transposing that term. It has doubtless been observed, in the solutions of the equations of § 24, that a term may be transposed from one member of an equation to the other by merely reversing its sign. This fact may be formally proved as follows : let any term of either...