Certainly! Let's solve the inequality step-by-step.
Given the inequality:
[tex]\[ x - 4 \geq -10 \][/tex]
Step 1: Isolate \( x \)
To isolate \( x \), we need to get rid of the \(-4\) on the left side. We can do this by adding 4 to both sides of the inequality:
[tex]\[ x - 4 + 4 \geq -10 + 4 \][/tex]
This simplifies to:
[tex]\[ x \geq -6 \][/tex]
Step 2: Write the solution in interval notation
The inequality \( x \geq -6 \) means that \( x \) can be any number greater than or equal to \(-6\). In interval notation, this is written as:
[tex]\[ [-6, \infty) \][/tex]
Step 3: Graph the solution set
To graph the solution set on the number line:
1. Draw a number line.
2. Place a closed circle (or solid dot) at \(-6\) to indicate that \(-6\) is included in the solution set.
3. Shade the number line to the right of \(-6\) to indicate that all numbers greater than \(-6\) are included in the solution.
Here's a graphical representation on a number line:
```
<----|----|----|----|----|----|----|----|----|----|----|---->
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
●==================>
```
In summary:
- The solution to the inequality \( x - 4 \geq -10 \) is \( x \geq -6 \).
- The interval notation for the solution is \([ -6, \infty )\).
- The graph of the solution set is a number line with a closed circle at [tex]\(-6\)[/tex] and shading to the right.
