Consider the following inequality:3x + 4 +7 > 13Step 1 of 2: Solve the absolute value inequality and express the solution in interval notationAnswerHow to enter your answer (Opens in new window)KeypadKeyboard ShortcutsSelecting a radio button will replace the entered answer value(s) with the radio button value. If the radiobutton is not selected, the entered answer is used.O No Solution

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CamellaQ44445 CamellaQ44445 · Answer 1 · 2022-10-28T22:44:33+02:00

Given:

[tex]3|x+4|+7>13[/tex]

To solve the given inequality, we subtract 7 from both sides first:

[tex]\begin{gathered} 3|x+4|+7>13 \\ 3|x+4|+7-7>13-3 \end{gathered}[/tex]

Simplify

[tex]\begin{gathered} 3|x+4|>6 \\ \frac{3|x+4|}{3}>\frac{6}{3} \\ |x+4|>2 \end{gathered}[/tex]

Next, we apply the absolute rule:

If |u| >a, a>0 then u<-a or u>a

So our equations would be:

x+4<-2

or

x+4>2

For x+4<-2:

[tex]\begin{gathered} x+4<-2 \\ \text{Simplify and rearrange} \\ x<-2-4 \\ x<-6 \end{gathered}[/tex]

For x+4>2:

[tex]\begin{gathered} x+4>2 \\ x>2-4 \\ x>-2 \end{gathered}[/tex]

Hence,

x<-6 or x>-2

Therefore, the interval notation is:

[tex](-\infty,-6)\cup(-2,\infty)[/tex]

The graph of the solution set is: