Solving First Inequality

We need to solve the first inequality:

$2x - 1 > 7$

• Add 1 to both sides: $2x - 1 + 1 > 7 + 1$ $2x > 8$
• Divide both sides by 2: $\frac{2x}{2} > \frac{8}{2}$ $x > 4$

So, the solution for the first inequality is $x > 4$.

Solving Second Inequality

Next, we solve the second inequality:

$2x - 9 < 1$

• Add 9 to both sides: $2x - 9 + 9 < 1 + 9$ $2x < 10$
• Divide both sides by 2: $\frac{2x}{2} < \frac{10}{2}$ $x < 5$

The solution for the second inequality is $x < 5$.

Combining Inequality Solutions

We need a value of $x$ that satisfies *both* inequalities simultaneously. This means $x$ must be greater than 4 AND less than 5.

Combining $x > 4$ and $x < 5$ gives the combined inequality:

$4 < x < 5$

Matching Option

Now, compare this result with the given options:

• Option 1: $x \le -4$
• Option 2: $-4 < x \le 4$
• Option 3: $4 < x < 5$
• Option 4: $x \ge 5$

The expression $4 < x < 5$ exactly matches Option 3.