What you’ll learn
Solve compound inequalities.
Key idea
Division by a negative coefficient reverses comparison directions; endpoint strictness remains attached to its corresponding boundary.
Negative division reverses directions and swaps endpoint correspondence; preserve each strict/inclusive boundary and operate on all three parts.
Worked example
Enter the exact value or ordered values in the format requested below.
Solve -8≤-5x-3≤17. Enter an ascending chained inequality for x with both endpoint types preserved.
- Subtract -3 from all three parts: -5≤-5x≤20.
- Divide every part by -5; reverse comparison directions for a negative divisor and reorder into increasing bounds. Solution -4≤x≤1; original upper threshold 17 occurs at x=-4.
Answer: -4≤x≤1
Quick Check
Evaluate a worked attempt at solve compound inequalities, identify the first invalid step, and provide the correction.
Solve -13<-5x-3<7: Step 1 subtracts -3 throughout to obtain -10<-5x<10. Step 2 replaces only -5x by x, leaving endpoints and comparison directions unchanged, claiming -10<x<10. Locate the first invalid step and correct the interval.