Question

Solve the compound inequality

-4x+60≥84 and x-3<7

Write the answer in interval notation

Answer 1

`-4x+60\geq84\qquad\text{subtract 60 from both sides}\\\\-4x\geq24\qquad\text{change the signs}\\\\4x\leq-24\qquad\text{divide both sides by 4}\\\\x\leq-6\to x\in(-\infty,\ -6]\\\\x-3<7\qquad\text{add 3 to both sides}\\\\x<10\to x\in(-\infty,\ 10)\\\\x\in(-\infty,\ -6]\ and\ x\in(-\infty,\ 10)\ then\ \boxed{x\in(-\infty,\ -6]}`