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

Question

Which number line is the correct representation of the solution?

Answer 1

To solve the inequality `-7 < 2x + 1 < 11`, we need to isolate the variable "x" in the middle of the inequality.

Starting with `2x + 1`:
Subtract 1 from each part of the inequality:
`2x + 1 - 1 < 11 - 1`
Simplifying:
`2x < 10`

Now, divide each part of the inequality by 2:
`2x/2 < 10/2`
Simplifying:
`x < 5`

So we have found that `x` must be less than 5.

Now, let's represent this on a number line.

We draw a number line and mark 5 as a point on the line.

Since `x` must be less than 5, we shade everything to the left of 5 on the number line to represent the solution.

The correct representation of the solution on the number line is as follows:

```
<---------|------------------------|----->
-7 5 11
```