Chapter 3.2, Problem 20PPE

To determine

The solution of given inequality $-3\ge x-1$ . Graph and check the solutions.

Answer to Problem 20PPE

  $x\le -2$

  

Explanation of Solution

Given information:

The given inequality is $-3\ge x-1$ .

Calculation:

Add $1$ on both the sides.

  $\begin{array}{c}-3+1\ge x-1+1\\ -2\ge x\\ x\le -2\end{array}$

Here, the closed circle is used because the inequality is “less than or equal to” $(\le )$ . The black arrow is drawn to the left of the point  $-2$ because these are the values that are less than or equal to $-2$ .

  

Substitute the end point $-2$ into the equation $-3=x-1$ .

  $\begin{array}{l}-3\stackrel{?}{=}-2-1\\ -3=-3\end{array}$

The above condition is true.

To check the inequality, select any number which is less than or equal to $-2$ .

Substitute the value of $x=-3$ in the given inequality $-3\ge x-1$ .

  $\begin{array}{l}-3\stackrel{?}{\ge }-3-1\\ -3\ge -4\end{array}$

The above condition is true.

Hence, the solution of the given inequality is all the real number less than or equal to $-2$ i.e. $\left(x\le -2\right)$ .