Question

`5(2x-7)+42-3x=2`

Answer 1

`\boxed{\sf x = - (5)/(7)}`

Explanation:

`\sf Solve \: for \: x: \\ \sf \implies 5(2x-7)+42-3x=2 \\ \\ \sf 5(2x - 7) = 10x - 35 : \\ \sf \implies \boxed{ \sf 10x - 35} - 3x + 42 = 2 \\ \\ \sf Grouping \: like \: terms, \: 10x - 35 - 3x + 42 = \\ \sf (10x - 3x) + ( - 35 + 42) : \\ \sf \implies \boxed{ \sf (10x - 3x) + ( - 35 + 42)} = 2 \\ \\ \sf 10x - 3x = 7x : \\ \sf \implies \boxed{ \sf 7x} + ( - 35 + 42) = 2 \\ \\ \sf 42 - 35 = 7 : \\ \sf \implies 7x + \boxed{ \sf 7} = 2 \\ \\ \sf Subtract \: 7 \: from \: both \: sides: \\ \sf \implies 7x + (7 - \boxed{ \sf 7}) = 2 - \boxed{ \sf 7} \\ \\ \sf 7 - 7 = 0 : \\ \sf \implies 7x = 2 - 7 \\ \\ \sf 2 - 7 = - 5 : \\ \sf \implies 7x = \boxed{ \sf - 5} \\ \\ \sf Divide \: both \: sides \: of \: 7x = - 5 \: by \: 7: \\ \sf \implies (7x)/(7) = ( - 5)/(7) \\ \\ \sf (7)/(7) = 1 : \\ \\ \sf \implies x = - (5)/(7)`

Answer 2

`\displaystyle x=- (5)/(7)`

Explanation:

`5(2x-7)+42-3x=2`

Expand brackets.

`10x-35+42-3x=2`

Combine like terms.

`10x-3x+42-35=2`

`7x+7=2`

Subtract 7 on both sides.

`7x+7-7=2-7`

`7x=-5`

Divide both sides by 7.

`(7x)/(7) =(-5)/(7)`

`x=- (5)/(7)`