To solve the compound inequality [tex]\(-26 \leq 4x - 2 < 22\)[/tex], we first want to isolate [tex]\(x\)[/tex]. We can start by breaking down the problem step-by-step.
1. Step 1: Add 2 to all parts of the inequality
[tex]\[
-26 \leq 4x - 2 < 22
\][/tex]
Adding 2 to each part, we get:
[tex]\[
-26 + 2 \leq 4x - 2 + 2 < 22 + 2
\][/tex]
Simplifying, this results in:
[tex]\[
-24 \leq 4x < 24
\][/tex]
2. Step 2: Divide all parts by 4
[tex]\[
-24 \leq 4x < 24
\][/tex]
Dividing each part by 4, we have:
[tex]\[
\frac{-24}{4} \leq \frac{4x}{4} < \frac{24}{4}
\][/tex]
Simplifying, this gives:
[tex]\[
-6 \leq x < 6
\][/tex]
The solution to the inequality is therefore [tex]\(x \in [-6, 6)\)[/tex], which means [tex]\(x\)[/tex] is greater than or equal to [tex]\(-6\)[/tex] and less than [tex]\(6\)[/tex].
In interval notation, we write the solution as:
[tex]\[
[-6, 6)
\][/tex]
