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1.Solve the inequality $2x - 5 \le -x +12$. Give your answer as an interval.

2.Solve the inequality $-4(x + 4) > x + 7.$ Give your answer as an interval.

Jun 29, 2020

#1
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This is AoPS homework.  You should not cheat on your homework.

Jun 29, 2020
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1.

$$2x - 5 \le -x +12\\ =3x\le17\\ =x\le\frac{17}{3}\\ \boxed{x\in(-\infty,\frac{17}{3}]}$$

2.

$$-4(x+4)>x+7\\ -4x-16>x+7\\ -5x>23\\ 5x<-23\\ x<-\frac{23}{5}\\\ \boxed{x\in(-\infty, -\frac{23}{5})}$$

Jun 29, 2020