To solve the inequality [tex]\(8 \leq x < 12\)[/tex], we need to identify the set of values for [tex]\(x\)[/tex] that satisfy both conditions:
1. [tex]\(x \geq 8\)[/tex]
2. [tex]\(x < 12\)[/tex]
Here’s a step-by-step solution:
### Step 1: Understanding the Inequality Components
The inequality consists of two parts:
- The first part, [tex]\(8 \leq x\)[/tex], tells us that [tex]\(x\)[/tex] must be greater than or equal to 8.
- The second part, [tex]\(x < 12\)[/tex], tells us that [tex]\(x\)[/tex] must be less than 12.
### Step 2: Combining the Conditions
We now combine these two parts to form a single compound inequality:
[tex]\[8 \leq x < 12\][/tex]
This inequality means that [tex]\(x\)[/tex] is in the range from 8 to 12 but does not include 12. So, [tex]\(x\)[/tex] can be any number starting from 8 up to, but not including, 12.
### Step 3: Identifying the Solution Set
To find the solution set, we list all the possible values of [tex]\(x\)[/tex] that satisfy the inequality [tex]\(8 \leq x < 12\)[/tex]. Since the inequality involves integers, we look for all integer values within this range.
The integer values that satisfy [tex]\(8 \leq x < 12\)[/tex] are:
- 8
- 9
- 10
- 11
### Step 4: Presenting the Solution Set
Therefore, the solution set for [tex]\(x\)[/tex] is:
[tex]\[
x = \{8, 9, 10, 11\}
\][/tex]
These are all the integer values that satisfy the given inequality [tex]\(8 \leq x < 12\)[/tex].
