To solve the compound inequality
13x−5<15x+4<7x+12, we need to break it into two separate inequalities and solve each part separately. Let's do this step by step:
1. Solve the first inequality:
13x−5<15x+4Subtract
13x from both sides of the inequality:
−5<2x+4Subtract 4 from both sides:
−9<2x Divide both sides by 2 :
−‌<xor equivalently
x>−‌ 2. Solve the second inequality:
15x+4<7x+12Subtract
7x from both sides of the inequality:
8x+4<12Subtract 4 from both sides:
8x<8Divide both sides by 8 :
x<1 Now, we combine the results of the two inequalities:
−‌<x<1Since
x∈W (set of whole numbers), the whole numbers in this interval are 0 . Therefore, the solution set is:
{0}Hence, the correct option is:
Option A:
{0}