An Introduction to Algebra Upon the Inductive Method of Instruction

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4. There is a pole i and i under water, and 5 feet out of water ; what is the length of the pole? « % Let X denot^ the whole length. Then ^-f-^ -f- 5 must be equal to the whole length. Hence, Reducing to a common denominator.
2^3^ 6x Sx . 2x, c.
46 Algebra, TL.
Adding together, y^^*^^ Since the two members are equal, if — be subtracted from 6 both, they will still be equal ; hence, 6 and 0? = 30 Ans, 30 feet.
Proof, One half of 30 is 15, and one third of thirty is 10. Now 30= 15 + 10 + 5.
There
... is another mode of reducing the above equation which in most cases is to be preferred. It is the same in principle.
If both members of an equation be multiplied by the same number, they evidently will still be equal.
In the equation, a;=f. +^+5.
First multiply both members by 2, the denominator of one of the fractions, and it becomes, 207 = 0? +?5+ 10. ^3^ Next multiply both members by 3, the denominator of the other fraction, and it becomes, 6a: = 3a? + 2o? + 30 or 6 a? = 5 0? + 3^* Subtracting 5 x from both members, ^ a?


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