Question

Solve:
3x-5/2 +x+ 2x-3/3 = 5/6 - 3x/2​

Answer 1

x = 26/45

Explanation:

Answer 2

Given Question

Solve for x :

`\rm :\longmapsto\:(3x - 5)/(2) + x + (2x - 3)/(3) = (5)/(6) - (3x)/(2)`

`\green{\large\underline{\sf{Solution-}}}`

Given expression is

`\rm :\longmapsto\:(3x - 5)/(2) + x + (2x - 3)/(3) = (5)/(6) - (3x)/(2)`

• On taking LCM of (2 and 3 = 6) on LHS and Taking LCM of ( 2 and 6 = 6) on RHS, we get

`\rm :\longmapsto\:(3(3x - 5) + 6x + 2(2x - 3))/(6) = (5 - 9x)/(6)`

`\rm :\longmapsto\:9x - 15 + 6x + 4x - 6 = 5 - 9x`

`\rm :\longmapsto\:(9x + 6x + 4x) - 15 - 6 = 5 - 9x`

`\rm :\longmapsto\:19x - 21 = 5 - 9x`

`\rm :\longmapsto\:19x + 9x = 5 + 21`

`\rm :\longmapsto\:28x = 26`

`\rm :\longmapsto\:x = (26)/(28)`

`\bf\implies \:x = (13)/(14)`

VERIFICATION

Consider LHS

`\rm :\longmapsto\:(3x - 5)/(2) + x + (2x - 3)/(3)`

On substituting the value of x, we get

`\rm \:  =  \: ((39)/(14) - 5)/(2) + (13)/(14) + ((13)/(7) - 3)/(3)`

`\rm \:  =  \: (39- 70)/(28) + (13)/(14) + (13 - 21)/(21)`

`\rm \:  =  \: ( - 31)/(28) + (13)/(14) - (8)/(21)`

`\rm \:  =  \: ( - 31 + 26)/(28) - (8)/(21)`

`\rm \:  =  \: ( -5)/(28) - (8)/(21)`

`\rm \:  =  \: ( -15 - 32)/(84)`

`\rm \:  =  \: - \: (47)/(84)`

Consider RHS

`\rm :\longmapsto\: (5)/(6) - (3x)/(2)`

On substituting the value of x, we get

`\rm \:  =  \: (5)/(6) - (39)/(28)`

`\rm \:  =  \: (70 - 117)/(84)`

`\rm \:  =  \: - (47)/(84)`

Hence, LHS = RHS

Hence, Verified.