How do you graph |x+4|<2 on a number line?

Question

How do you graph |x+4|<2 on a number line?

Answer 1

Step 1: Solve the absolute value inequality. For absolute values you need to have two possible outcomes:

Outcome #1:

x + 4 &lt; 2

x &lt; 2 - 4

x &lt; -2 (&lt;==ANSWER!!)

Outcome #2:

x + 4 &gt; -2

x &gt; -2 - 4

x &gt; -6 (&lt;==ANSWER!!)

Step 2: Since the answers are NOT &quot;equal to&quot; any specific number, you will need to draw an &quot;open point&quot; on the values gotten from the answers in Step 1.

Say this is a number line

|-----|-----|-----|-----|-----|-----|-...

-6...-5...-4...-3...-2...-1...0...1......

Represent each value

º......................º

|-----|-----|-----|-----|-----|-----|-...

-6...-5...-4...-3...-2...-1...0...1......

Now, the answer states that x &lt; -2 and that x &gt; -6. This means that -6 &lt; x &lt; -2

So the &quot;x&quot; is greater than -6 AND less than -2.

On the number line, trace a line denoting where the x &quot;lives&quot;.

º----------------------º

|-----|-----|-----|-----|-----|-----|-...

-6...-5...-4...-3...-2...-1...0...1......

And done :-)

Hope I helped!

Answer 2

first you need to solve the inequality

-2 less (x+4) less 2

-6 less (x) less -2

( -6,-2)

When you draw the number line you will start from -6 to -2  and with open circle in the endpoints