Question

SOLVE FOR X???


`(x)/(3) +2 =(x)/(4)+3`


`3(4+2x)=33 - x`

Answer 1

`\boxed{ \bold{ \boxed{ \sf{1. \: \: \: \: \: x = 12}}}}`

`\boxed{ \bold{ \boxed{ \sf{2. \: \: \: \: \: x = 3}}}}`

Explanation:

`\sf{1. \: \: \: \: (x)/(3) + 2 = (x)/(4) + 3}`

Move x / 4 to left hand side and change its sign

Similarly, move 2 to right hand side and change it's sign

`\longrightarrow{ \sf{ (x)/(3) - (x)/(4) = 3 - 2}}`

Take the L.C.M of 3 and 4

L.C.M of 3 and 4 = 12

`\longrightarrow{ \sf{ (x * 4 - x * 3)/(12) = 3 - 2}}`

`\longrightarrow{ \sf{ (4x - 3x)/(12) = 3 - 2}}`

`\longrightarrow{ \sf{ (x)/(12) = 3 - 2}}`

Subtract 2 from 3

`\longrightarrow{ \sf{ (x)/(12) = 1}}`

Do cross multiplication

`\longrightarrow{ \sf{x = 1 * 12}}`

`\longrightarrow { \sf{x = 12}}`

--------------------------------------------------------------------

`\sf{2. \: \: \: \: 3(4 + 2x) = 33 - x }`

Distribute 3 through the parentheses

`\longrightarrow{ \sf{12 + 6x = 33 - x}}`

Move x to left hand side and change it's sign

Similarly, move 12 to right hand side and change it's sign

`\longrightarrow{ \sf{6x + x = 33 - 12}}`

Collect like terms

`\longrightarrow{ \sf{7x = 33 - 12}}`

Subtract 12 from 33

`\longrightarrow{ \sf{7x = 21}}`

Divide both sides by 7

`\longrightarrow{ \sf{ (7x)/(7) = (21)/(7) }}`

Calculate

`\longrightarrow{ \sf{x = 3}}`

Hope I helped!

Best regards! :D