Certainly! Let's solve the inequality involving the given expression [tex]\(9x - 22\)[/tex].
### Step-by-Step Solution:
1. Write Down the Inequality:
We start with an inequality involving the given expression [tex]\((9x - 22) > 0\)[/tex].
2. Isolate [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], we need to manipulate the inequality such that [tex]\(x\)[/tex] is on one side of the inequality symbol.
[tex]\(9x - 22 > 0\)[/tex]
3. Add 22 to Both Sides:
Add 22 to both sides of the inequality to start isolating [tex]\(x\)[/tex].
[tex]\(9x - 22 + 22 > 0 + 22\)[/tex]
This simplifies to:
[tex]\(9x > 22\)[/tex]
4. Divide Both Sides by 9:
To solve for [tex]\(x\)[/tex], divide both sides of the inequality by 9.
[tex]\(\frac{9x}{9} > \frac{22}{9}\)[/tex]
This simplifies to:
[tex]\(x > \frac{22}{9}\)[/tex]
5. Interpret the Inequality:
The solution to our inequality is [tex]\(x > \frac{22}{9}\)[/tex]. In interval notation, this is written as:
[tex]\(\left( \frac{22}{9}, \infty \right)\)[/tex]
### Conclusion:
The inequality we wrote and solved describes the set of possible values for [tex]\(x\)[/tex] such that [tex]\((9x - 22) > 0\)[/tex]. Therefore, the solution to the inequality is:
[tex]\[ x > \frac{22}{9} \][/tex]
In interval notation, this is:
[tex]\[ \left( \frac{22}{9}, \infty \right) \][/tex]
