Question

solve for q and graph the solution.
3 > |q + 1|
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.
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4

Explanation:

Step1: Recall absolute value inequality rule

For \(|x| < a\) (where \(a>0\)), the solution is \(-a < x < a\). Here, \(x = q + 1\) and \(a = 3\), so we have \(-3 < q + 1 < 3\).

Step2: Solve the left inequality

Subtract 1 from both sides of \(-3 < q + 1\): \(-3 - 1 < q + 1 - 1\), which simplifies to \(-4 < q\).

Step3: Solve the right inequality

Subtract 1 from both sides of \(q + 1 < 3\): \(q + 1 - 1 < 3 - 1\), which simplifies to \(q < 2\).

Step4: Combine the solutions

From Step2 and Step3, we get \(-4 < q < 2\).

To graph this, we use open circles at \(-4\) and \(2\) (since the inequality is strict, not \(\leq\)) and draw a line segment between them.

Answer:

The solution for \(q\) is \(-4 < q < 2\). For the graph, place open circles at \(-4\) and \(2\) on the number line and connect them with a line segment.