Question

graph the solution to the inequality on the number line.\\(|u - 5| < 5\\)

Explanation:

Step1: Solve absolute value inequality

The absolute value inequality \(|u - 5| < 5\) can be rewritten as a compound inequality. For \(|x| < a\) (where \(a>0\)), it is equivalent to \(-a < x < a\). So here, we have \(-5 < u - 5 < 5\).

Step2: Solve for u

Add 5 to all parts of the compound inequality.
For the left side: \(-5 + 5 < u - 5 + 5\), which simplifies to \(0 < u\).
For the right side: \(u - 5 + 5 < 5 + 5\), which simplifies to \(u < 10\).
So the solution to the inequality is \(0 < u < 10\).

To graph this on the number line:

• We use an open circle at \(u = 0\) (because the inequality is strict, \(u

eq0\)) and an open circle at \(u = 10\) (because \(u
eq10\)).

• Then we draw a line segment connecting the two open circles to represent all the values of \(u\) between 0 and 10.

Answer:

The solution to the inequality \(|u - 5| < 5\) is \(0 < u < 10\). On the number line, there are open circles at 0 and 10, with a line segment between them.