Chapter 3.2, Problem 3P

To determine

To find: The solutions of the inequality $-1\ge y+12$ and graph them.

Answer to Problem 3P

The solutions of the inequality are all real numbers left to $-13$ including it and graph is shown in Figure (1).

Explanation of Solution

Given information: The given inequality is $-1\ge y+12$ .

Calculation:

Subtract 12 from both the sides of the given inequality and simplify.

  $\begin{array}{c}-1\ge y+12\\ -1-12\ge y+12-12\\ -13\ge y\end{array}$

So, the solutions of $-13\ge y$ are all real numbers to the left of $-13$ . To check that the endpoint $-13$ is the solution of the inequality, substitute it in the equation $-1=y+12$ .

  $\begin{array}{c}-1=y+12\\ -1=-13+12\\ -1=-1\end{array}$

The solutions of $-13\ge y$ are all real numbers left to $-13$ and $-13$ .

The graph of the solutions of the given inequality is shown below:

    Figure (1)

Therefore, the solutions of the inequality are all real numbers left to $-13$ including it and graph is shown in Figure (1).