If 2x/3 - [5(4x/5 - 4/3)]/2 = 1/3, then what is the value of x
(1) 9/4 (2) 4/9 (3)-9/4 (4) -4/9 (5) None of these
Answers
Answer:
Option (1)
Step-by-step explanation:
Given :-
2x/3 - [5(4x/5 - 4/3)]/2 = 1/3
To find :-
What is the value of x ?
Solution :-
Given equation is
(2x/3) - [5(4x/5)-(4/3)]/2 = 1/3
=> (2x/3) - [5×4{(x/5)-(1/3)}]/2 = 1/3
=> (2x/3) - [20{(x/5)-(1/3)}]/2 = 1/3
LCM of 5 and 3 = 15
=> (2x/3) - [ 20{(3x-5)/15}]/2 = 1/3
=> (2x/3) - [ 20(3x-5)/(15×2)] = 1/3
=> (2x/3) - [ 20(3x-5)/30] = 1/3
=> (2x/3) - [ 2(3x-5)/3] = 1/3
=> (2x/3) - [ (6x-10)/3] = 1/3
=> [2x-(6x-10)]/3 = 1/3
=> (2x-6x+10)/3 = 1/3
=> (-4x+10)/3 = 1/3
On cancelling 3 both sides then
=> -4x+10 = 1
=> -4x = 1-10
=> -4x = -9
=> 4x = 9
=> x = 9/4
Therefore, x = 9/4
Answer:-
The value of x for the given problem is 9/4
Check:-
If x = 9/4 then LHS of the given equation is
=>[2(9/4)/3] - [ 5{(4(9/4))/5 -(4/3)}]/2
=> [(9/2)/3] - [ 5{(9/5) - (4/3)}]/2
=> (9/6) - [ 5{27-20)/15)]/2
=> (3/2) - [5(7/15)]/2
=> (3/2) - [ (7/3)]/2
=> (3/2) - [7/(3×2)]
=> (3/2) - (7/6)
=> (3/2)-(7/6)
=> (9-7)/6
=> 2/6
=> 1/3
=> RHS
LHS = RHS is true for x = 9/4
Verified the given relations in the given problem.