Question

The solution set for the inequality $ 13x - 5 \leq 15x + 4<7x + 12;  x \in W $

• A. \( \{ 0 \} \)
• B. \( \{ 0, 1 \} \)
• C. \( \{ \} \)
• D. \( \{-4, -3, -2, -1, 0 \} \)

Hint:

When solving inequalities with multiple parts, always treat them separately, then combine the results while considering the constraints on the solution set (such as integer or whole numbers).

Answer 1

The Correct Option is A

We are given the inequality: \[ 13x - 5 \leq 15x + 4<7x + 12 \] Let's first solve each part of the inequality separately. 
Step 1: Solving the first part \( 13x - 5 \leq 15x + 4 \):
\[ 13x - 15x \leq 4 + 5 \] \[ -2x \leq 9 \] \[ x \geq -\frac{9}{2} \] 
Step 2:
Solving the second part \( 15x + 4 < 7x + 12 \): \[ 15x - 7x<12 - 4 \] \[ 8x<8 \] \[ x<1 \] 
Step 3: Combining both inequalities:
We have the solution to the system of inequalities as: \[ -\frac{9}{2} \leq x<1 \] However, since \( x \in W \) (where \( W \) is the set of whole numbers), the only valid value for \( x \) in this range is \( x = 0 \). Thus, the solution set is \( \{ 0 \} \).