Question

solve for d and graph the solution.
2 ≥ |d + 1|
click two endpoints to graph a line segment, an endpoint and an arrowhead to graph ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to empty circles, click on them.

Explanation:

Step1: Recall absolute value inequality rule

For \(|x| \leq a\) (where \(a\geq0\)), it is equivalent to \(-a \leq x \leq a\). Here, the inequality is \(2 \geq |d + 1|\), which can be rewritten as \(|d + 1| \leq 2\).

Step2: Apply the rule to the inequality

Using the rule, we get \(-2 \leq d + 1 \leq 2\).

Step3: Solve the left - hand inequality

Subtract 1 from both sides of \(-2 \leq d + 1\): \(-2-1\leq d+1 - 1\), so \(-3\leq d\).

Step4: Solve the right - hand inequality

Subtract 1 from both sides of \(d + 1\leq2\): \(d+1 - 1\leq2 - 1\), so \(d\leq1\).

Answer:

The solution for \(d\) is \(-3\leq d\leq1\). To graph this, we would plot a line segment with endpoints at \(d=-3\) (filled - in circle) and \(d = 1\) (filled - in circle) on the number line.