Solve: −7≤2x+1<11 Which number line is the correct representation of the solution?

Answer 1

In order to find the solution, we need to solve the given inequality. To do this, we need to isolate x:

-7 ≤ 2x + 1 < 11

Subtracting 1 from all parts of the inequality, we get:

-7 - 1 ≤ 2x + 1 - 1 < 11 - 1

Simplifying, we have:

-8 ≤ 2x < 10

Now, dividing all parts of the inequality by 2, we get:

-8/2 ≤ 2x/2 < 10/2

Simplifying further, we have:

-4 ≤ x < 5

This means that x can take any value greater than or equal to -4, but less than 5.

To represent this on a number line, we need to mark a closed circle at -4 (since it is included in the inequality) and an open circle at 5 (since it is not included). Then, we draw a line between these two points to represent the range of x values. Therefore, the correct representation on the number line is as follows:

-4 | 5