Chapter 3.2, Problem 17PPE

To determine

The solution of given inequality $t-4\ge -7$ . Graph and check the solutions.

Answer to Problem 17PPE

  $t\ge -3$

  

Explanation of Solution

Given information:

The given inequality is $t-4\ge -7$ .

Calculation:

Add $4$ on both the sides.

  $\begin{array}{c}t-4+4\ge -7+4\\ t\ge -3\end{array}$

Here, the closed circle is used because the inequality is “greater than or equal to” $(\ge )$ . The black arrow is drawn to the right of the point  $-3$ because these are the values that are greater than or equal to $-3$ .

  

Substitute the end point $-3$ into the equation $t-4=-7$ .

  $\begin{array}{r}-3-4\stackrel{?}{=}-7\\ -7=-7\end{array}$

The above condition is true.

To check the inequality, select any number which is greater than or equal to $-3$ .

Substitute the value of $t=-2$ in the given inequality $t-4\ge -7$ .

  $\begin{array}{r}-2-4\stackrel{?}{\ge }-7\\ -6\ge -7\end{array}$

The above condition is true.

Hence, the solution of the given inequality is all the real number greater than or equal to $-3$ i.e. $\left(t\ge -3\right)$ .