Chapter 1.4, Problem 10CYU

To determine

To write: the algebraic expression for given verbal expression and then to simplify.

Answer to Problem 10CYU

The expression is $\frac{1}{2}\left(4y+y+3\right)$ and is simplified to $\frac{5y+3}{2}$

Explanation of Solution

Given information:

Consider the “ one half of $4$ times y plus the quantity of y and $3$ ”

Calculations:

Write the expression

  $4$ times y $\Rightarrow 4y$

  $4$ times y plus the quantity of y and $3$$\Rightarrow 4y+y+3$

one half of $4$ times y plus the quantity of y and $3$ $\Rightarrow \frac{1}{2}\left(4y+y+3\right)$

Simplify the expression

  $\begin{array}{l}\Rightarrow \frac{1}{2}\left(4y+y+3\right)=\Rightarrow \frac{1}{2}\text{(4y)+}\frac{1}{2}(y)+\frac{1}{2}(3)\text{ distributive property }\\ =2y+\frac{y}{2}+\frac{3}{2}\\ =\frac{4y+y+3}{2}\\ =\frac{5y+3}{2}\end{array}$

Hence, the expression is $\frac{1}{2}\left(4y+y+3\right)$ and is simplified to $\frac{5y+3}{2}$