$12 \leqslant 3(x-2)<15$
Answer (2)
Divide all parts of the inequality by 3: 4 l e q s l an t x − 2 < 5 .
Add 2 to all parts of the inequality: 6 l e q s l an t x < 7 .
The solution to the inequality is 6 l e q s l an t x < 7 .
The range of x is 6 l e q s l an t x < 7 .
Explanation
Understanding the Problem We are given the inequality 12 l e q s l an t 3 ( x − 2 ) < 15 and we want to find the range of values for x that satisfy this inequality.
Dividing by 3 First, we divide all parts of the inequality by 3: 3 12 ⩽ 3 3 ( x − 2 ) < 3 15
Simplifying Simplifying the inequality, we get: 4 ⩽ x − 2 < 5
Adding 2 Next, we add 2 to all parts of the inequality: 4 + 2 ⩽ x − 2 + 2 < 5 + 2
Final Range Simplifying again, we find the range of x : 6 ⩽ x < 7 So, x is greater than or equal to 6 and less than 7.
Conclusion Therefore, the solution to the inequality is 6 ⩽ x < 7 .
Examples
Imagine you're planning a daily budget for a week-long vacation. You know you want to spend at least $12 but no more than $15 each day on activities, and you also need to factor in a fixed cost of $2 per day for transportation. This inequality helps you determine the range of spending money you can allocate for activities each day, ensuring you stay within your budget while accounting for transportation costs. By solving the inequality, you find the minimum and maximum amount you can spend on activities each day to meet your overall budget goals.
The solution to the inequality 12 ⩽ 3 ( x − 2 ) < 15 is 6 ⩽ x < 7 . This means that values of x can start at 6 and go up to, but not including, 7. Thus, any number between these two values satisfies the inequality.
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