Choose any number. - Add $3$, then multiply the result by $4$. - Subtract twice your original nu

Question

Choose any number. - Add $3$, then multiply the result by $4$. - Subtract twice your original number. - Subtract $12$. - Divide the result by $2$. Test the trick using $5$ and using $-2$. Let the original number be $n$. Write one expression for the entire trick and simplify it. Explain the result. If “add $3$” is changed to “add $7$”, what number should replace $12$ so that the trick still returns the original number? Justify your answer.

Accepted Answer

(b) $\frac{4(n+3)-2n-12}{2}$; The trick always returns the original number: the constants cancel, leaving twice the original number before the final division by $2$. (c) $28$

Algebraic Expressions, Identities and Formulae

Algebraic Expressions, Identities and Formulae

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