Question

Twice the difference of a number and 7 is equal to 9. What is the number?

Answer 1

`x=11 1/2 " "->" "23/2`

Explanation:

Breaking the question down into its component parts.

Twice the `" "->2xx(?)`
difference of `->2xx(?-?)`
a number `" "->2xx(x-?)`
and 7`" "->2xx(x-7)`
is equal to `" "->2xx(x-7)=?`
9 `" "->2xx(x-7)=9`

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Given:`" "2(x-7)=9`

Divide both sides by 2

`" "2/2(x-7)=9/2`

`" "x-7=9/2`

Add 7 to both sides

`" "x-7+7=9/2+7`

but -7+7=0

`" "x+0=9/2+7`

`" "x=11 1/2 " "->" "23/2`

Answer 2

x=11.5

Explanation:

Suppose the number is x, then 2*(x-7) =9, as per the statement made in the question.

Solving this for x, gives, `x-7=9/2`. This means `x=23/2` or 11.5