Final answer:
To solve the inequality 'Two times a number +1 is greater than five and less than seven,' we let x represent the unknown number, resulting in the numerical range where x is greater than 2 and less than 3.
Step-by-step explanation:
The mathematical inequality given, “Two times a number +1 is greater than five and less than seven”, can be translated into an algebraic expression to find the range of the unknown number. Here are the steps:
- Let the unknown number be represented by the variable x.
- Translate the verbal statement into an algebraic expression: 2x + 1 > 5 and 2x + 1 < 7.
- To find the range for x when 2x + 1 > 5, we subtract 1 from both sides giving us 2x > 4, thus x > 2.
- To find the range for x when 2x + 1 < 7, we subtract 1 from both sides giving us 2x < 6, thus x < 3.
- Therefore, the solution is x > 2 and x < 3, meaning x is between 2 and 3.
This solution uses the rules for inequalities and the addition of positive numbers to solve the inequality.