Chapter 5.5, Problem 4BGP

To determine

Tosolve:The given equation

Answer to Problem 4BGP

  $p\le 23$

  

Explanation of Solution

Given information:

  $2p+5\ge 3\left(p-6\right)$

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:

  $\begin{array}{l}2p+5\ge 3\left(p-6\right)\\ \Rightarrow 2p+5\ge 3p-3·6\mathrm{...}\left(\text{Distributive property}\right)\\ \Rightarrow 2p+5\ge 3p-18\\ \Rightarrow 2p+5-2p\ge 3p-18-2p\mathrm{...}\left(\text{subtraction property of inequality}\right)\\ \Rightarrow 5\ge p-18\\ \Rightarrow 5+18\ge p-18+18\mathrm{...}\left(\text{addition property of inequality}\right)\\ \Rightarrow 23\ge p\\ \Rightarrow p\le 23\end{array}$

Graph:

In the inequality $p\le 23$ we can say $p$ in smaller than or equal to 23 and can plot the same on number line-

We will make a closed dot on 23 as it is included in the inequality and then move towards left as $p$ in smaller than 23.