Question

Solve the following equation


$\frac{9x + 0.5}{5} - \frac{2x + 3}{4} = 0$
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$\frac{x - 1}{2} + \frac{2x - 1}{4} = \frac{x - 1}{3} - \frac{2x - 1}{6}$
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Answer 1

Step-by-step explanation:

Solutions :-

1) Given equation is

(9x+0.5)/5-(2x+3)/4 = 0

LCM of 5 and 4 is 20

=> [4(9x+0.5)-5(2x+3)]/20 = 0

=> [(36x+2.0)-(10x+15)]/20 = 0

=> (36x+2-10x-15)/20 = 0

=> (26x-13)/20 = 0

=> 26x-13 = 0×20

=> 26x-13 = 0

=>>26x = 13

=> x = 13/26

=> x = 1/2

Solution of the given equation is 1/2

Check :-

If x = 1/2 then

LHS = (9x+0.5)/5 -(2x+3)/4

=>[9(1/2)+0.5]/5 - [2(1/2)+3]/4

=>[(9/2)+0.5]/5 -[1+3]/4

=> (4.5+0.5)/5 -(4/4)

=> (5/5)-(4/4)

=> 1-1

=> 0

=> RHS

LHS = RHS is true for x = 1/2

2)

Given equation is (x-1)/2 +(2x-1)/4 = (x-1)/3-(2x-1)/6

LCM of 2 and 4 = 4

LCM of 3 and 6 = 6

=>[ 2(x-1)+(2x-1)]/4 = [2(x-1)-(2x-1)]/6

=> (2x-2+2x-1)/4 = (2x-2-2x+1)/6

=> (4x-3)/4 =-1/6

On applying cross multiplication then

=> 6(4x-3) = 4×-1

=> 24x-18 = -4

=> 24x = -4+18

=> 24x = 14

=> x = 14/24

=> x = 7/12

Solution of the given equation is 7/12

Check :-

If x = 7/12

LHS = (x-1)/2 +(2x-1)/4

=>[(7/12)-1]/2 + [2(7/12)-1]/4

=> (7-12)/2 + (14-12)/4

=> -5/2 + 2/4

=>-5/2 + 1/2

=> (-5+1)/2

=> -4/2

=> -2

RHS =(x-1)/3-(2x-1)/6

=> [(7/12)-1)]/3 - [2(7/12)-1]/6

=>>(7-12)/3 -(14-12)/6

=> (-5/3)-(2/6)

=> -5/3 -1/3

=> (-5-1)/3

=> -6/3

=> -2

LHS = RHS is true for x =7/12

Answer:-

I)Solution of the given equation is 1/2

ii)Solution of the given equation is 7/12

Answer 2

Step-by-step explanation:

1.     $\sf{\dfrac{9x+0.5}{5} - \dfrac{2x+3}{4} = 0}$

$\implies \sf{\dfrac{9x+0.5}{5} = \dfrac{2x+3}{4}}$

$\implies \sf{4(9x+0.5) = 5(2x+3)}$

$\implies \sf{36x+2 = 10x+15}$

$\implies \sf{ 36x - 10x = 15 - 2}$

$\implies \sf{ 26x = 13}$

$\implies \sf{ x = \dfrac{13}{26}}$

$\implies \sf{ x = \dfrac{1}{2}}$

2.    $\sf{\dfrac{x-1}{2} + \dfrac{2x-1}{4} = \dfrac{x-1}{3} - \dfrac{2x-1}{6}}$

$\implies \sf{ \dfrac{2(x-1) + (2x-1)}{4} = \dfrac{2(x-1) - (2x-1)}{6} }$

$\implies \sf{ \dfrac{(2x-2) + (2x-1)}{4} = \dfrac{(2x-2) - (2x-1)}{6} }$

$\implies \sf{ \dfrac{2x-2 + 2x-1}{4} = \dfrac{2x - 2 -2x+1}{6} }$

$\implies \sf{ \dfrac{4x-3}{4} = \dfrac{- 1}{6} }$

$\implies \sf{6(4x-3) = - 1 \times 4 }$

$\implies \sf{24x-18 = -4 }$

$\implies \sf{24x=18-4 }$

$\implies \sf{24x=14 }$

$\implies \sf{x = \dfrac{14}{24} }$

$\implies \sf{x = \dfrac{7}{12} }$