Solve: `-7<2x+1<11`

Answer 1

To solve this compound inequality, we'll solve each inequality separately.

First, let's solve `-7 < 2x + 1`:
Subtract 1 from both sides:
-7 - 1 < 2x + 1 - 1
-8 < 2x

Next, divide both sides by 2:
-8/2 < 2x/2
-4 < x

So, one part of the solution is `x > -4`.

Now let's solve `2x + 1 < 11`:
Subtract 1 from both sides:
2x + 1 - 1 < 11 - 1
2x < 10

Next, divide both sides by 2:
2x/2 < 10/2
x < 5

So, the other part of the solution is `x < 5`.

Combining both parts of the solution, we have `-4 < x < 5`.