Chapter 15.1, Problem 16PSC

(a)

To determine

To Find: The restrictions on the measure of the original angle.

Answer to Problem 16PSC

  $x>\frac{25}{4}$

Explanation of Solution

Given:

  $\begin{array}{l}x>3y+7\\ y>6-x\end{array}$

Formula Used:

  $a\left(c+d\right)=ac+ad$

Calculation:

  $\begin{array}{l}x>3y+7\\ y>6-x\\ x>3\left(6-x\right)+7\\ \text{⇒}x>18-3x+7\\ \text{⇒}x+3x>18+7\\ \text{⇒}4x>25\\ \text{⇒}x>\frac{25}{4}\end{array}$

Conclusion:

Thus, the required restrictions is $x>\frac{25}{4}$ .

(b)

To determine

To Find: The restrictions on the measure of the original angle.

Answer to Problem 16PSC

  $y>-\frac{1}{4}$

Explanation of Solution

Given:

  $\begin{array}{l}x>3y+7\\ y>6-x\end{array}$

Formula Used:

  $a\left(c+d\right)=ac+ad$

Calculation:

  $\begin{array}{l}\text{⇒}y>6-\left(3y+7\right)\\ \text{⇒}y>6-3y-7\\ \text{⇒}y+3y>-1\\ \text{⇒}4y>-1\\ \text{⇒}y>-\frac{1}{4}\end{array}$

Conclusion:

Thus, the required restrictions is $y>-\frac{1}{4}$ .