Certainly! Let's solve the inequality [tex]\( -2 < 5x - 2 \)[/tex] step by step.
1. Start with the given inequality:
[tex]\[
-2 < 5x - 2
\][/tex]
2. Add 2 to both sides of the inequality to isolate the term with [tex]\( x \)[/tex] on one side:
[tex]\[
-2 + 2 < 5x - 2 + 2
\][/tex]
Simplify both sides:
[tex]\[
0 < 5x
\][/tex]
3. Divide both sides by 5 to solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{0}{5} < \frac{5x}{5}
\][/tex]
Simplify:
[tex]\[
0 < x
\][/tex]
Therefore, the solution to the inequality [tex]\( -2 < 5x - 2 \)[/tex] is [tex]\( x > 0 \)[/tex].
4. Express the solution in interval notation:
[tex]\[
x \in (0, \infty)
\][/tex]
So, the solution in interval notation is [tex]\( (0, \infty) \)[/tex].
