...with its sign changed. We can proceed in a like manner in any other case. Hence the general rule : 52. Any term may be transposed from one side of an equation to the other, provided its sign is changed. 53. Any term, therefore, which occurs on both sides with the same sign...

...= - (+ a). Also, since AC - AB = BC, and ÄC = BC + ÄB; it follows that a vector may be tranferred from one side of an equation to the other by changing its sign. 14°. Since BC + AB =ÄC, 12°, it follows that directions can be assigned to the sides of any triangle,...

...equation that we abbreviate into the mechanical form and call it Transposition. Any term of an equation may be transposed from one side of an equation to the other, provided the sign of the term be changed. The main object of transposition of terms is to get all the...

...and changed its sign. We can proceed in like manner in any other case. Hence, the general rule : 53. Any term may be transposed from one side of an equation to the other, provided its sign is changed. It follows from axioms 1 and 2 that : 54. Any term that occurs with the...

...= c (5) then a+bb=cb (6) or, a = c — b (7) From this it is evident that we may carry over a term from one side of an equation to the other by changing its sign ; for, in equation (5) the positive quantity b, is on the left-hand side of the equation, whereas in equation...

...multiplied by equals, the products are equal. 4. If equals are divided by equals, the quotients are equal. Any term may be transposed from one side of an equation to the other by changing its sign. Thus : 3 x — 8 = x + 12. Therefore, 3 x — x = 12 + 8, and 2 x = 20, and x = 10. In this example,...

...Study the solutions of Exs. 130 and 131 until you see the truth of the following principle: A quantity may be transposed from one side of an equation to the other if the sign prefixed to the quantity is changed from plus to minus or from minus to plus. When no sign...

...2, and we have x — a + a = b + a. That is, x = b + a. applies to any term of an equation. Hence, any term may be transposed from one side of an equation to the other, provided its sign is changed. If we transpose all the terms of the equation a — x = b — c, we have...

...equation, and all the other terms to the other side. This process is called transposing the terms. 56. Any term may be transposed from one side of an equation to the other provided the sign of the term is changed. 1. Find the number for which x stands when x - b = a. •...

...ж8-1/а-га. 3. Solve the equation : — 4. How would you show that any quantity may be transferred from one side of an equation to the other by changing its sin? 5. Find the value of — /vY + ^54" _ /Vf-^Sy \Vf~-Vb) ' W7 + V5/' 6. Find the square root of...