Q15. - Algebra 2

Question

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

15. $n+4\ge -7$

Step-by-Step Solution

Answer

Solution of inequality $n+4\ge -7$ is $n\ge -11$

In interval form, solution set is $\left[-11,\infty \right)$

Solution set on number line is 

Step 1 - Write properties of inequality

Properties of inequalities are written in following table:

Step 2 - Simplify n + 4 ≥ − 7

To simplify given inequality, use subtraction property of inequalities. Subtract by same number does not change the sign of inequality as shown below

$\begin{array}{c}n+4\ge -7\\ n+4-4\ge -7-4\\ n\ge -11\end{array}$

Step 3 - Write solution set

The solution set of the inequality contains all real numbers greater than or equal to $-11$ 

As, $-11$ is included in the set so bracket is used with it whereas $\infty$ is not included so parentheses is used with it.

In interval form solution set is $\left[-11,\infty \right)$ 

Step 4 - Graph the solution set

As solution set of the inequality is all real numbers greater than or equal to $-11$

So arrow is towards $\infty$ and dot on $-11$ shows it is included in the solution set.