Chapter 1, Problem 7PT

To determine

To evaluate: the given expression.

Answer to Problem 7PT

The value of the expression is 3.5.

Explanation of Solution

Given information:

Given expression

  $2\left|3y-8\right|+y$

And

  $y=2.5$

Concept used:

Absolute value of a function a is given by

  $\left|a\right|=\{\begin{array}{l}aa>0\\ -aa<0\\ 0a=0\end{array}$ \

And

  $\begin{array}{l}\left|-a\right|=a\\ \left|a\right|=a\end{array}$

Calculation:

Consider the given expression.

  $2\left|3y-8\right|+y$

Substitute the value of $y$ in the given expression,

  $\begin{array}{c}2\left|3y-8\right|+y=2\left|3\cdot 2.5-8\right|+2.5\\ =2\left|-\frac{1}{2}\right|+2.5\\ =2\cdot \frac{1}{2}+2.5\\ =1+2.5\\ =3.5\end{array}$

Hence, the value of the expression is 3.5.