what is the solution to the inequality |x - 4| < 3?\n-7 < x < -1\n1 < x < 7\nx < -7 or x < -1\nx > 1 or x < 7
what is the solution to the inequality |x - 4| < 3?\n-7 < x < -1\n1 < x < 7\nx < -7 or x < -1\nx > 1 or x < 7
Answer
Explanation:
Step1: Recall absolute - value rule
If (|a|\lt b) ((b>0)), then (-b < a < b). Here (a=x - 4) and (b = 3), so (-3<x - 4<3).
Step2: Solve the compound inequality
Add 4 to all parts of (-3<x - 4<3). We get (-3+4<x-4 + 4<3 + 4), which simplifies to (1<x<7).
Answer:
B. (1<x<7)