Solve: -7 < 2x + 1 < 11
Which number line is the correct representation of the solution?
To solve the inequality -7 < 2x + 1 < 11, we need to isolate x in the middle of the two inequalities.
First, we subtract 1 from all parts of the inequality:
-7 - 1 < 2x + 1 - 1 < 11 - 1
-8 < 2x < 10
Then we divide all parts of the inequality by 2 (since the coefficient of x is 2):
-8/2 < 2x/2 < 10/2
-4 < x < 5
The solution to the inequality is -4 < x < 5.
The correct representation of this solution on a number line is as follows:
<----(-4)---------------(5)---->
So the correct number line representation has an open circle at -4 and an open circle at 5, and the region between the two open circles is shaded.