Chapter 5.5, Problem 36PPS

To determine

To solve:The given inequality and graph it.

Answer to Problem 36PPS

  $-9\ge r$

  

Explanation of Solution

Given information:

  $3\left(3r+5\right)\ge 24+10r$

Concept Used:

When two quantities are not equal, the comparison between them is often presented by certain symbols, this comparison is known as inequality and the symbols used for such comparison are known as inequality symbols.

There are four inequality symbols, $>$ , $<$ , $\ge$ , $\le$ namely “greater than”, “less than”, “greater than or equal to” and “less than or equal to” respectively.

On a number line, integers are placed at an interval of one and value if integers increases as we move left to right on the number line.

Calculation:

  $\begin{array}{l}3\left(3r+5\right)\ge 24+10r\\ \Rightarrow 3\left(3r\right)+3\left(5\right)\ge 24+10r\\ \Rightarrow 9r+15\ge 24+10r\\ \Rightarrow 9r+15-24\ge 24+10r-24\\ \Rightarrow 9r-9\ge 10r\\ \Rightarrow 9r-9-9r\ge 10r-9r\\ \Rightarrow -9\ge r\end{array}$

Graph:

In the inequality $-9\ge r$ we can say $r$ in smaller than or equal to $-9$ and can plot the same on number line-

We will make a closed dot on $-9$ as it is not included in the inequality and then move towards left as $r$ in smaller than $-9$ .