To solve the inequality:

$8x - 10 > 5$

Follow these steps:

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Step 1: Isolate the variable term.

Add $10$ to both sides:

$8x > 5 + 10$

Simplify:

$8x > 15$

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Step 2: Solve for $x$.

Divide both sides by $8$ (since $8 > 0$, the inequality direction remains unchanged):

$x > \frac{15}{8}$

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Step 3: Simplify (if needed).

Convert $\frac{15}{8}$ to a mixed number or decimal:

$x > 1.875$

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Final Answer:

$x > \frac{15}{8} \quad \text{or} \quad x > 1.875$

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Notes:

• The solution represents all values of $x$ greater than $1.875$.
• If you graph it on a number line, you'd place an open circle at $1.875$ and shade the region to the right.

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Would you like me to verify this solution with examples or graph it? Let me know!

Related Questions:

1. How do you solve inequalities with negative coefficients?
2. How do you graph solutions for linear inequalities?
3. What happens when you multiply/divide inequalities by negative numbers?
4. Can you solve $8x - 10 \geq 5$ and explain the difference?
5. How do you write inequality solutions in interval notation?

Tip:

When solving inequalities, remember to flip the inequality sign if multiplying or dividing by a negative number!