Chapter 15.1, Problem 2PSA

(a)

To determine

To Justify: The variable in the given expression.

Answer to Problem 2PSA

  $x<18$

Explanation of Solution

Given:

  $\begin{array}{l}x+y<30\\ y=12\end{array}$

Formula Used:

  $a\left(c+d\right)=ac+ad$

Calculation:

  $\begin{array}{l}x+y<30\\ y=12\\ \text{⇒}x+y<30\\ \text{⇒}x+12<30\\ \text{⇒}x<30-12\\ \text{⇒}x<18\end{array}$

Conclusion:

Thus, the required solution is $x<18$ .

(b)

To determine

To Justify: The variable in the given expression.

Answer to Problem 2PSA

  $18<x$

Explanation of Solution

Given:

  $\begin{array}{l}x+y=30\\ y<12\end{array}$

Formula Used:

  $a\left(c+d\right)=ac+ad$

Calculation:

  $\begin{array}{l}x+y=30\\ y<12\\ \text{⇒}x+y=30\\ \text{⇒}y=30-x\\ \text{⇒}30-x=y<12\\ \text{⇒}30-x<12\\ \text{⇒}30-12<x\\ \text{⇒}18<x\end{array}$

Conclusion:

Thus, the required solution is $18<x$ .