Chapter 1.7, Problem 53P

Write a word phrase for each expression. Then simplify each expression.

$2(n+1)$

To determine

To write:A word phrase for $2(n+1)$ and simplification.

Answer to Problem 53P

A word phrase for $2(n+1)$ is

“Twice the sum of n and 1”

The solution is $2n+2$

Explanation of Solution

Given information: $2(n+1)$

Calculation:

The expression $(n+1)$ indicates “sum of n and 1”.

The expression $2(n+1)$ indicates “twice $(n+1)$ ”.

Thus, a word phrase for $2(n+1)$ is

“Twice the sum of n and 1”

  $\begin{array}{l}2(n+1)\\ =(2\times n)+(2\times 1)[\because a(b+c)=(a\times b)+(a\times c)]\\ =(2n)+(2)\\ =2n+2\end{array}$

Thus, the solution is $2n+2$