Question

How do you solve `(9w - 4) ( w - 5) = 0`?

Answer 1

`w=4/9 and w=5` are both solutions

Explanation:

Multiply any value by 0 and the answer is 0

So this must mean that both
`(9w-4)=0` and `(w-5)=0` are solutions

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Consider:`" "9w-4=0`

Add `color(red)(4)` to both sides

`color(green)(9w-4color(red)(+4)" "=" "0color(red)(+4)`

but `-4+4=0` giving

`9w=4`

Divide both sides by `color(red)(9)`

`color(green)(9/(color(red)(9)) w=4/(color(red)(9))`

But `9/9=1 and 1xxw=w` giving:

`w=4/9`
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Consider:`" "w-5=0`

Add `color(red)(5)` to both sides

`color(green)(w-5color(red)(+5)" "=" "0color(red)(+5))`

but `-5+5=0`

`w=5`
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`color(blue)("Method summery")`

If what you wish to move to the other side of = is add or subtract change it to 0.

If what you wish to move to the other side of = is multiply or divide change it to 1