Question

Consider the following inequalities.
\text{(i) } 2x - 1 \(>\) 7
\text{(ii) } 2x - 9 \(<\)1
Which one of the following expressions below satisfies the above two inequalities?

• A. \( x \leq -4 \)
• B. \( -4<x \leq 4 \)
• C. \( 4<x<5 \)
• D. \( x \geq 5 \)

Hint:

When solving inequalities, always isolate \(x\) and combine the results of multiple inequalities to find the common solution.

Answer 1

The Correct Option is C

We are given two inequalities: \[ \text{(i) } 2x - 1>7 \quad \text{and} \quad \text{(ii) } 2x - 9<1 \] We will solve each inequality and then find the common solution. Step 1: Solve the first inequality.
From the inequality \( 2x - 1>7 \), we add 1 to both sides: \[ 2x>8 \] Now, divide both sides by 2: \[ x>4 \]
Step 2: Solve the second inequality.
From the inequality \( 2x - 9<1 \), we add 9 to both sides: \[ 2x<10 \] Now, divide both sides by 2: \[ x<5 \]
Step 3: Combine the two results.
We now have: \[ x>4 \quad \text{and} \quad x<5 \] Thus, the solution is \( 4<x<5 \).
Step 4: Conclusion.
The correct option is (C) \( 4<x<5 \).