Maths-
General
Easy

Question

Solve for x-
(3/7)(1−2x)/2 = 12 19/27

hintHint:

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
an = a × a × ... × a                    n times.
2. A fraction represented with its quotient and remainder is a mixed fraction.
In the given sum, quotient = 12, remainder = 19 & Divisor = 27.
∴ The given mixed fraction can be written as- (Quotient × Divisor + Remainder) / Divisor = (12×27) + 19 / 27 = 343/27

The correct answer is: x = 7/2 or 3.5 for the given equation.


    Step-by-step solution:-
    (3/7)(1−2x)/2 = 12 19/27
    ∴ (3/7)(1−2x)/2 = 343/27
    ∴ (3/7)(1−2x)/2 = 73 / 33
    ∴ (3/7)(1−2x)/2 = (7/3)3
    ∴ (3/7)(1−2x)/2 = (3/7)-3 ….................................... (b-n = 1/bn)
    ∴ (1−2x)/2 = -3 …............................................... (Exponents of the same base in an equation are equal)
    ∴ 1-2x = -3×2
    ∴ 1-2x = -6
    ∴ -2x = -6 -1
    ∴ -2x = -7
    ∴ x = -7/-2
    ∴ x = 7/2
    Final Answer:-
    ∴ x = 7/2 or 3.5 for the given equation.

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