Question

How do you solve `-6.5b + 8.5+ 3b = 27.5`?

Answer 1

As with any algebraic equation, clump the variables on one side (it is preferable if the coefficient of the variable is positive, but it doesn't really matter).

`-6.5b+8.5+3b=27.5`
`-3.5b=19`
`b=19/-3.5`
`b=-5.43` (3s.f.)

Answer 2

`b=-38/7`
The question does not state that we may use an approximate answer (rounding a decimal). You may or may not loose marks in an exam. Risky!

Explanation:

Don't like decimals so lets get rid of them.

Multiply both sides by 10

`-65b+85+30b=275`

Regrouping:

`(30b-65b)+85=275`

`color(white)("d")-35b color(white)("dddd") +85=275`

Subtract 85 from both sides

`-35b=+190`

Note that when dividing, if the signs are the same, the result is positive.

Divide both sides by `(-35)`

`+b=(+190)/(-35)`

`b=-38/7color(red)( larr" More precise than a rounded decimal")`

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