Solve: `-7\le2x+1<11`

Question

Which number line is the correct representation of the solution?

Answer 1

To solve the inequality `-7\le2x+1<11`, we first need to isolate the variable.

-7 ≤ 2x + 1 < 11

Subtract 1 from all parts:
-7 - 1 ≤ 2x + 1 - 1 < 11 - 1
-8 ≤ 2x < 10

Now, divide all parts by 2:
-8/2 ≤ 2x/2 < 10/2
-4 ≤ x < 5

So, the solution to the inequality is -4 ≤ x < 5.

The correct representation on the number line would be a closed circle at -4 and an open circle at 5. Then draw a horizontal line between -4 and 5 to represent all the values of x within that range.