Question

solve the inequality. then graph the solution set on a number line.
part 1 of 2
solve the absolute value inequality. if there is no solution, click on
o solution\. if the solution is all real numbers, click on \all real\.
part 2 of 2
the solution set is graphed as

Explanation:

Step1: Analyze the inequality \(|y + 4|>3\)

The absolute value inequality \(|A|>B\) (where \(B>0\)) is equivalent to \(A > B\) or \(A<-B\). Here, \(A = y + 4\) and \(B = 3\). So we can split the inequality into two cases:
Case 1: \(y + 4>3\)
Case 2: \(y + 4<-3\)

Step2: Solve Case 1: \(y + 4>3\)

Subtract 4 from both sides of the inequality:
\(y+4 - 4>3 - 4\)
\(y>-1\)

Step3: Solve Case 2: \(y + 4<-3\)

Subtract 4 from both sides of the inequality:
\(y + 4-4<-3 - 4\)
\(y<-7\)

Answer:

The solution to the inequality \(|y + 4|>3\) is \(y < - 7\) or \(y>-1\). To graph this on the number line:

• For \(y < - 7\), we draw an open circle at \(-7\) (since \(-7\) is not included in the solution) and shade the region to the left of \(-7\).
• For \(y>-1\), we draw an open circle at \(-1\) (since \(-1\) is not included in the solution) and shade the region to the right of \(-1\).