Question

The solution for the following system of inequalities \( 3x - 7 < 5 + x \) and \( 11 - 5x \leq 1 \) on a real number line is

• A. A
• B. B
• C. C
• D. D

Hint:

While dividing inequalities by a negative number, always reverse the inequality sign.

Answer 1

The Correct Option is A

Step 1: Solve first inequality.
\[ 3x - 7 < 5 + x \]
\[ 3x - x < 5 + 7 \]
\[ 2x < 12 \Rightarrow x < 6 \]

Step 2: Solve second inequality.
\[ 11 - 5x \leq 1 \]
\[ -5x \leq 1 - 11 \]
\[ -5x \leq -10 \]

Step 3: Divide by negative number (reverse sign).
\[ x \geq 2 \]

Step 4: Combine both inequalities.
\[ x \geq 2 \quad \text{and} \quad x < 6 \]

Step 5: Write solution set.
\[ 2 \leq x < 6 \]

Step 6: Represent on number line.
Closed circle at \( 2 \), open circle at \( 6 \), shaded between them.

Step 7: Final Answer.
\[ \boxed{[2,6)} \]