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Solve the inequality for [tex][tex]$x$[/tex][/tex]:
[tex]-2 \ \textless \ 5x - 2[/tex]

Simplify your answer as much as possible.

Sagot :

GinnyAnswer
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].
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