Question

How do you solve `\frac { 3} { 6} ( 4x - 8) = 7x - 25`?

Answer 1

`x=21/5`

Explanation:

`"simplify and distribute the bracket on the left side"`

`rArr1/2(4x-8)=7x-25`

`rArr2x-4=7x-25`

`"subtract 7x from both sides"`

`2x-7x-4=cancel(7x)cancel(-7x)-25`

`rArr-5x-4=-25`

`"add 4 to both sides"`

`-5xcancel(-4)cancel(+4)=-25+4`

`rArr-5x=-21`

`"divide both sides by"-5`

`(cancel(-5) x)/cancel(-5)=(-21)/(-5)`

`rArrx=21/5`

`color(blue)"As a check"`

Substitute this value into the equation and if both sides are equal then it is the solution.

`"left "=1/2(84/5-40/5)=1/2xx44/5=22/5`

`"right "=147/5-125/5=22/5`

`rArrx=21/5" is the solution"`

Answer 2

`21/5` = `4 1/5`

Explanation:

`3/6(4x-8)=7x-25`

or, `3/6 xx4x-3/6 xx8 = 7x-25`

or, `cancel3^1/cancel6^2 xx4x -3/cancel6^3 xxcancel8^4 = 7x-25`

or, `1/cancel2^1 xxcancel4^2x-cancel3^1/cancel3^1 xx4 = 7x-25`

or, `2x-4=7x-25`

Bring the `x` terms to one side and number terms to other side of equal to sign.

or, `2x-7x=-25+4` (bringing any term from one side of equal to sign to other side causes the sign/mathematical operator to change it to its opposite sign. Which is `+` becomes `-` and `xx` becomes `/` or vice -versa.

or, `-5x = -21`

or `x = -21/-5` = `21/5` (the negative signs in the numerator and denominator get cancelled out)

or, `x` = `21/5` = `4 1/5`