Question

solve for u and graph the solution. 3 ≥ |u - 1| click two endpoints to graph a line segment, an endpoint and ray, or two arrowheads to graph a line. to change endpoints from circles, click on them.

Explanation:

Step1: Recall absolute value inequality rule

For \(|x| \leq a\) (where \(a \geq 0\)), it is equivalent to \(-a \leq x \leq a\). Here, our inequality is \(3 \geq |u - 1|\), which can be rewritten as \(|u - 1| \leq 3\).

Step2: Apply the rule to solve for \(u\)

Using the rule from Step 1, we have \(-3 \leq u - 1 \leq 3\).

Step3: Solve the left inequality

Add 1 to all parts of the compound inequality. For the left part: \(-3 + 1 \leq u - 1 + 1\), which simplifies to \(-2 \leq u\).

Step4: Solve the right inequality

For the right part: \(u - 1 + 1 \leq 3 + 1\), which simplifies to \(u \leq 4\).

Step5: Combine the results

Combining the two inequalities from Step 3 and Step 4, we get \(-2 \leq u \leq 4\).

Answer:

The solution for \(u\) is \(-2 \leq u \leq 4\). To graph this, we would plot a line segment with endpoints at \(-2\) and \(4\) on the number line (both endpoints are closed circles since the inequality is inclusive).