Solving Algebraic Formulae

General strategy of solving variable in algebraic formulae

Example:

Given that

t−p = r , express t in terms of p and r. r + 2t

Use the following strategy: - If there’s any , square both sides of the equation to eliminate

( )

.

2

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-

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( a = b → (a ) 2 = b → a 2 = b If there’s any fraction, use cross multiplication to turn the equation into fractiona c → ad = bc ) free (non-fractional) form. ( = b d Ask yourself what to find? If the terms containing the variable you want are being ‘locked’ by another expression, just expand them to ‘release’ the terms! bt − b = ab − at (Express t in terms of the others: b(t − 1) = a (b − t ) → Group all terms containing the variable you want at one side of the equation solely. → bt + at = ab + b ) ( bt − b = ab − at Factorise ‘out’ the variable from the expression bt + at → t (b + a ) Divide both sides of the equation by the unwanted factor resulted from the previous factorisation in order to obtain the final answer. t (b + a ) ab + b ab + b → → ( t (b + a ) = ab + b = t= b+a b+a b+a

Solution: t−p =r r + 2t

⇒

Cross-multiplication

t− p r = r + 2t 1

(t – p)(1) = (r + 2t)(r) t − p = r 2 + 2tr

Expand – release terms containing t

t − p + (- 2tr ) = r 2 + 2tr + (- 2tr ) (t − 2tr ) − p = r 2

Group all t-terms solely at one side

(t − 2tr ) − p + ( p ) = r 2 + ( p ) t − 2tr = r 2 + p

Factorise out the t

t (1 − 2r ) = r + p 2

t (1 − 2r ) r 2 + p = 1 − 2r 1 − 2r t=

r2 + p 1 − 2r

Divide both sides by unwanted factor

Answer