Question

solve for y and graph the solution. 1 < |y + 5| click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to empty circles, click on them. not feeling ready yet? these can help: work it out

Explanation:

Step1: Recall absolute - value inequality rule

For \(|a|>b\) (\(b > 0\)), it is equivalent to \(a>b\) or \(a < - b\). Here \(a=y + 5\) and \(b = 1\), so we have \(y+5>1\) or \(y + 5<-1\).

Step2: Solve \(y+5>1\)

Subtract 5 from both sides: \(y+5-5>1 - 5\), which simplifies to \(y>-4\).

Step3: Solve \(y + 5<-1\)

Subtract 5 from both sides: \(y+5-5<-1 - 5\), which simplifies to \(y<-6\).

Answer:

The solution is \(y < - 6\) or \(y>-4\). On the number - line, we mark an open circle at \(y=-6\) and draw an arrow to the left, and mark an open circle at \(y = - 4\) and draw an arrow to the right.