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Chapter 6: Problem 18

Solve each inequality and graph the solution set on a number line. \(x+4 \geq 0\)

Short Answer

Expert verified
The solution set to the inequality \(x+4 \geq 0\) is \(x \geq -4\). On the number line, this is represented by a closed circle at -4 with a line extending to the right.

Step by step solution

01

Isolate the x

In order to find the solution set to the inequality \(x+4 \geq 0\), the first step is to isolate \(x\) on one side. This can be done by subtracting 4 from both sides of the inequality, which results in \(x \geq -4\).
02

Draw the Number Line

The second step is to graph the solution set on a number line. Start by drawing a straight line that represents the number line, and mark down the number -4 on it.
03

Graphing the Solution Set

Because the inequality is \(x \geq -4\), this means x is equal to -4 or any number greater than -4. On the number line, we represent -4 with a closed circle (because it's included in the solution set) and draw a line going to the right from -4 (representing all the numbers greater than -4)

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