Chapter 3.2, Problem 24PPE

To determine

The solution of given inequality $y-1\ge 1.5$ . Graph and check the solutions.

Answer to Problem 24PPE

  $y\ge 2.5$

  

Explanation of Solution

Given information:

The given inequality is $y-1\ge 1.5$ .

Calculation:

Add $1$ on both the sides.

  $\begin{array}{c}y-1+1\ge 1.5+1\\ y\ge 2.5\end{array}$

Here, the closed circle is used because the inequality is “greater than or equal to” $(\ge )$ . The black arrow is drawn to the right of the point  $2.5$ because these are the values that are greater than or equal to $2.5$ .

  

Substitute the end point $2.5$ into the equation $y-1=1.5$ .

  $\begin{array}{r}2.5-1\stackrel{?}{=}1.5\\ 1.5=1.5\end{array}$

The above condition is true.

To check the inequality, select any number which is greater than or equal to $2.5$ .

Substitute the value of $y=3$ in the given inequality $y-1\ge 1.5$ .

  $\begin{array}{r}3-1\stackrel{?}{\ge }1.5\\ 2\ge 1.5\end{array}$

The above condition is true.

Hence, the solution of the given inequality is all the real number greater than or equal to $2.5$ i.e. $\left(y\ge 2.5\right)$ .