Question

solve for d and graph the solution.\\(|d + 50| \leq 50\\)\\(\\)click two endpoints to graph a line segment, an endpoint and an arrowhead t\\(\\)ray, or two arrowheads to graph a line. to change endpoints from filled - in circles t\\(\\)circles, click on them.\\(\\)\\(-100\\) \\(-90\\) \\(-80\\) \\(-70\\) \\(-60\\) \\(-50\\) \\(-40\\) \\(-30\\) \\(-20\\) \\(-10\\) \\(0\\) \\(10\\)

Explanation:

Step1: Recall absolute value inequality rule

For \(|x| \leq a\) (where \(a \geq 0\)), it is equivalent to \(-a \leq x \leq a\). So for \(|d + 50| \leq 50\), we can apply this rule.

Step2: Solve the compound inequality

Substitute \(x = d + 50\) and \(a = 50\) into the rule. We get \(-50 \leq d + 50 \leq 50\).
First, subtract 50 from all parts of the inequality: \(-50 - 50 \leq d + 50 - 50 \leq 50 - 50\).
Simplify each part: \(-100 \leq d \leq 0\).

To graph this solution:

• The left endpoint is at \(d=-100\) (a filled - in circle since the inequality is non - strict, \(\leq\)) and the right endpoint is at \(d = 0\) (also a filled - in circle). We draw a line segment connecting these two points on the number line.

Answer:

The solution for \(d\) is \(-100 \leq d \leq 0\). To graph, plot filled - in circles at \(-100\) and \(0\) on the number line and draw a line segment between them.