Solve -7<2x+1<11 which number line is the correct repression of the solution

Answer 1

To solve the inequality -7 < 2x + 1 < 11, we need to isolate x.

First, let's subtract 1 from all parts of the inequality:

-7 - 1 < 2x + 1 - 1 < 11 - 1

Simplifying, we have:

-8 < 2x < 10

Next, let's divide all parts of the inequality by 2:

-8/2 < 2x/2 < 10/2

-4 < x < 5

Now we have x between -4 and 5, excluding the endpoints (-4 and 5).

To graph this on a number line, we draw a line segment that goes from -4 to 5, and indicate with open circles at -4 and 5 to exclude them. Then we shade the region between the two open circles to represent the solution.

Here is the correct representation on the number line:

<---|--------------( )-----( )---------------->
-4 5

The shaded region between -4 and 5 (excluding -4 and 5) represents the solution to the inequality -7 < 2x + 1 < 11.