$3 < 2a + 9 \leq 7$
Answer (2)
Subtract 9 from all parts of the inequality: − 6 < 2 a ≤ − 2 .
Divide all parts of the inequality by 2: − 3 < a ≤ − 1 .
The solution to the inequality is − 3 < a ≤ − 1 .
The range of possible values for a is − 3 < a ≤ − 1 .
Explanation
Understanding the Inequality We are given the inequality 3 < 2 a + 9 l e q s l an t 7 and we want to find the range of possible values for a .
Isolating the Term with a First, we subtract 9 from all parts of the inequality to isolate the term with a :
3 − 9 < 2 a + 9 − 9 l e q s l an t 7 − 9
Simplified Inequality This simplifies to: − 6 < 2 a l e q s l an t − 2
Solving for a Next, we divide all parts of the inequality by 2 to solve for a :
2 − 6 < 2 2 a l e q s l an t 2 − 2
Final Range for a This simplifies to: − 3 < a l e q s l an t − 1
Conclusion Therefore, the solution to the inequality is − 3 < a l e q s l an t − 1 . This means that a can take any value greater than − 3 and less than or equal to − 1 .
Examples
Imagine you're adjusting the temperature in a room. The inequality 3 < 2 a + 9 ⩽ 7 is like setting the thermostat within a certain range. Here, 'a' represents the adjustment you make. By solving the inequality, you determine the exact range of adjustments that keep the room's temperature within the desired comfort zone. This concept is useful in many real-life situations, such as managing budgets, controlling inventory levels, or optimizing production processes.
To solve the inequality 3 < 2 a + 9 ≤ 7 , we isolate a and find that the solution is − 3 < a ≤ − 1 . This indicates that a can take values greater than − 3 and up to − 1 . Understanding this concept can help with practical applications in everyday problem-solving.
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