# How do you solve b/2 - b/5 =6?

##### 1 Answer
Nov 4, 2016

$b = 20$

Takes longer to explain than do the actual maths.

#### Explanation:

Multiply by 1 and you do not change the overall value. However, 1 comes in many forms so you can change the way a number looks without changing its overall value.

" "color(green)([b/2color(red)(xx1)]" "-" "[b/5color(red)(xx1)]=6)

" "color(green)([b/2color(red)(xx5/5)]" "-" "[b/5color(red)(xx2/2)]=6)

$\text{ "[(5b)/10]" "-" "[(2b)/10]" } = 6$

$\text{ "(3b)/10" "=" } 6$

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Multiply both sides by $\textcolor{red}{\text{ } 10}$

" "color(green)(color(red)(10xx)(3b)/10" "=" "color(red)(10xx)6 )

$\text{ "10/10xx3b" "=" } 60$

$\textcolor{w h i t e}{.}$

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But $\frac{10}{10} = 1$

$\text{ "3b" "=" } 60$

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Divide both sides by 3

$\text{ "b" "=" } 20$