Question

solve the inequality and graph the solution.
1 ≤ (u/2) - 1
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
<--|-5---|-4---|-3---|-2---|-1---|0---|1---|2---|3---|4---|5--->

Explanation:

Step1: Add 1 to both sides

To isolate the term with \( u \), we add 1 to both sides of the inequality \( 1 \leq \frac{u}{2} - 1 \). This gives us \( 1 + 1 \leq \frac{u}{2} - 1 + 1 \), which simplifies to \( 2 \leq \frac{u}{2} \).

Step2: Multiply both sides by 2

To solve for \( u \), we multiply both sides of the inequality \( 2 \leq \frac{u}{2} \) by 2. This gives us \( 2\times2 \leq \frac{u}{2}\times2 \), which simplifies to \( 4 \leq u \) or \( u \geq 4 \).

Answer:

The solution to the inequality is \( u \geq 4 \). To graph this, we plot a closed dot at \( u = 4 \) (since the inequality is "greater than or equal to") and draw a ray to the right of 4 on the number line.