Chapter 2.4, Problem 38E

To determine

To find: the true point(s) satisfying the given inequality.

Answer to Problem 38E

  $\left(3,2\right)$

Explanation of Solution

Given information:

The inequality is $x+y\ge 3$ .

The given points are $\left(0,0\right),\left(3,2\right),\left(-4,2\right)$ or $\left(-2,4\right)$ .

Calculation:

Put $\left(0,0\right)$ in the inequality and solve as follows:

  $\begin{array}{c}x+y\ge 3\\ 0+0\ge 3\\ 0\ge 3\end{array}$

  $\therefore \text{ Do not satisfy}$

Put $\left(3,2\right)$ in the inequality and solve as follows:

  $\begin{array}{c}x+y\ge 3\\ 3+2\ge 3\\ 5\ge 3\end{array}$

  $\therefore \text{ It satisfies the inequality}$

Put $\left(-4,2\right)$ in the inequality and solve as follows:

  $\begin{array}{c}x+y\ge 3\\ -4+2\ge 3\\ -2\ge 3\end{array}$

  $\therefore \text{ Do not satisfy}$

Put $\left(-2,4\right)$ in the inequality and solve as follows:

  $\begin{array}{c}x+y\ge 3\\ -2+4\ge 3\\ 2\ge 3\end{array}$

  $\therefore \text{ Do not satisfy}$

Thus, the point satisfying the given inequality is $\left(3,2\right)$ .