Math Problem -3<2x+1<5

Question

I can't solve it

Answer 1

We need to manipulate the inequality so as to get just x in the middle instead of 2x+1.

So let’s subtract 1 from each term: -4<2x<4.

Now divide through by 2: -2<x<2.

That is the answer: x lies between -2 and 2.

A quick check will prove if this is right. Pick a value of x between the limits, say x=0. Put this in the original inequality: -3<1<5. Yes, that’s true, 1 does lie between -3 and 5, half way in fact.

Now let’s pick a value on the limit. We expect this to fail because we have <, not ≤. Pick x=2. The inequality -3<5<5 is not true because 5=5 not 5<5. The same applies if x=-2, when we get -3<-3, which isn’t true. So the answer -2<x<2 is correct.