consider the equation 1/( x2) = 4/ 3 . Jeffrey solves this equation as follows:

Question

consider the equation
1/( x2) = 4/ 3
. Jeffrey solves this equation as follows:
                                                          1/( x2) =4/ 3
                                                            x2 = 3/ 4
                                                        x2+2 = 3/ 4 +2
                                                              x = 11/ 4
(a) Write Jeffrey’s equation-solving process as a sequence of English-language statements, explaining the algebraic reasoning embedded in each step.
(b) At the end of his solution process, Jeffrey concludes that the only solution of the equation is x = 11/4. Is Jeffrey correct? Justify your answer.

Explanation / Answer

Given that, Jeffrey solves this equation as follows:
                                                          1/( x2) =4/ 3
                                                            x2 = 3/ 4 ........step(1)
                                                        x2+2 = 3/ 4 +2 ......step(2)
                                                              x = 11/ 4 ........step(3)

PART (a)-

step (1) is a cross multiplication for gating x-2 in Numerator

In the step (2) for elimination of -2 in left hand of the equation, he is adding 2 in both side of the equation. He is adding 2 both side, because from mathematical rule of sum we can add anything in the equation but we has do same thing in both side.

In the step (3) after eliminating -2 (in left hand side), he is calculating sum of 3/4 and 2 by L.C.M. and geting 11/4 (in right hand side).

PART (b)

Yes Jeffrey is correct. Because here x has only 1 dgree that means only one value of x can satisfy this equation.

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