Solve $18 \leq 2 d+8<34$
Answer (1)
Subtract 8 from all parts: 18 − 8 ≤ 2 d + 8 − 8 < 34 − 8 , which simplifies to 10 ≤ 2 d < 26 .
Divide all parts by 2: 2 10 ≤ 2 2 d < 2 26 .
Simplify the inequality: 5 ≤ d < 13 .
The solution is 5 ≤ d < 13 , meaning d can be any number from 5 up to (but not including) 13. 5 ≤ d < 13
Explanation
Understanding the Inequality We are given the compound inequality 18 ≤ 2 d + 8 < 34 . Our goal is to isolate d to find the range of values it can take.
Subtracting 8 First, we subtract 8 from all parts of the inequality to isolate the term with d : 18 − 8 ≤ 2 d + 8 − 8 < 34 − 8
Simplifying the Inequality This simplifies to: 10 ≤ 2 d < 26
Dividing by 2 Next, we divide all parts of the inequality by 2 to solve for d : 2 10 ≤ 2 2 d < 2 26
Final Solution This simplifies to: 5 ≤ d < 13
Examples
Imagine you're planning a party and need to buy enough snacks for each guest. You know that each guest will eat at least 5 snacks but definitely fewer than 13 snacks. This inequality helps you determine the possible range of snacks each person might consume, helping you plan your purchases effectively. Understanding inequalities is crucial in everyday scenarios like budgeting, time management, and resource allocation, ensuring you stay within desired limits.
