Question

solve for u and graph the solution. 5 ≤ |5u - 10| click two endpoints to graph a line segment, an endpoin ray, or two arrowheads to graph a line. to change endpoints circles, click on them.

Explanation:

Step1: Recall absolute value inequality rule

For \(|x| \geq a\) (where \(a>0\)), it is equivalent to \(x \geq a\) or \(x \leq -a\). Here, our inequality is \(5 \leq |5u - 10|\), which can be rewritten as \(|5u - 10| \geq 5\). So we have two cases:
Case 1: \(5u - 10 \geq 5\)
Case 2: \(5u - 10 \leq -5\)

Step2: Solve Case 1: \(5u - 10 \geq 5\)

Add 10 to both sides: \(5u - 10 + 10 \geq 5 + 10\)
Simplify: \(5u \geq 15\)
Divide both sides by 5: \(\frac{5u}{5} \geq \frac{15}{5}\)
So, \(u \geq 3\)

Step3: Solve Case 2: \(5u - 10 \leq -5\)

Add 10 to both sides: \(5u - 10 + 10 \leq -5 + 10\)
Simplify: \(5u \leq 5\)
Divide both sides by 5: \(\frac{5u}{5} \leq \frac{5}{5}\)
So, \(u \leq 1\)

Answer:

The solution for \(u\) is \(u \leq 1\) or \(u \geq 3\). To graph this, we would have a ray starting at \(1\) (with a closed circle) going to the left and a ray starting at \(3\) (with a closed circle) going to the right on the number line.