two interval notation questions

Question

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

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

have fun!

xplosions Jul 1, 2020

amazingxin777 · Answer 1 · 2020-07-01T06:42:34

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plz post a question at a time

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It's just two, not a big deal in my opinion. Any more than that would be an overload.

gwenspooner85 · Answer 2 · 2020-07-01T06:50:28

1.

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

2. $-4(x+4)>x+7\\ =-4x-16>x+7\\ =5x<-23\\ x<-\frac{23}{5}\\ \boxed{x\in(-\infty, -\frac{23}{5})}$

xplosions · Answer 3 · 2020-07-01T06:53:36

first one is right, but the second one is wrong. Try again!

xplosions · Answer 4 · 2020-07-01T09:30:43

Oh you're right! I put a bracket on the back instead of a close paranthesis. Sorry!