Question

1. $20x - 14 < x - 14 leq 16 - 5x$

Explanation:

Step1: Solve left inequality \(20x - 14 < x - 14\)

Subtract \(x\) and add \(14\) to both sides: \(20x - x < -14 + 14\)
Simplify: \(19x < 0\)
Divide by \(19\): \(x < 0\)

Step2: Solve right inequality \(x - 14 \leq 16 - 5x\)

Add \(5x\) and add \(14\) to both sides: \(x + 5x \leq 16 + 14\)
Simplify: \(6x \leq 30\)
Divide by \(6\): \(x \leq 5\)

Step3: Find intersection of solutions

Left solution: \(x < 0\); Right solution: \(x \leq 5\)
Intersection: \(x < 0\) (since \(x < 0\) is stricter than \(x \leq 5\) for \(x < 0\))

Answer:

The solution to the compound inequality is \(x < 0\)