Final answer:
To solve the inequality -3 < 2x + 1 < 7 for the number x, subtract 1 from all parts and then divide by 2. The solution is the range of numbers greater than -2 and less than 3.
Step-by-step explanation:
The problem statement here results in an inequality that can be expressed algebraically. If 'x' represents the unknown number, we can write the inequality as -3 < 2x + 1 < 7.
To solve for 'x', we will isolate the variable on one side by following the rules of inequalities similar to solving equations.
First, subtract 1 from all parts of the inequality to get the pure inequality without a constant.
-4 < 2x < 6
Now, divide all parts of the inequality by 2, which yields:
-2 < x < 3
All numbers greater than -2 and less than 3 satisfy the original problem statement. Therefore, the range of numbers that solve the inequality is from -2 to just below 3.