Math CentralQuandaries & Queries


Question from walter, a parent:

i'm a parent helping my daughter can you do a step by step on this equation been out of school for years thanks (4w-28)+(11w+13)=180 thanks

Hi Walter,

You have the equation $(4w-28)+(11w+13)=180$ and you want to find a sequence of equivalent equations that ends with $w = \mbox{ something.}

First of all you can remove the parentheses on the left side of the equation so that it becomes


Gathering the terms containing $w$ gives $4w+11w=15w.$ Also on the left you have $-28+13=-15$ so the equation becomes


You only want terms involving $w$ on the left side so add 15 to each side to obtain


and hence


Finally multiply each side by $\frac{1}{15}$ to get

\[\frac{1}{15}\times 15w=\frac{1}{15}\times195\]


\[w = 13.\]


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