Solve the inequality for $t$.
$3(4-2 t) \geq 15$
Answer (1)
Distribute the 3: 12 − 6 t g e 15 .
Subtract 12 from both sides: − 6 t g e 3 .
Divide by -6 (and flip the inequality sign): tl e − 2 1 .
The solution to the inequality is tl e − 2 1 .
Explanation
Understanding the Problem We are given the inequality 3 ( 4 − 2 t ) g e 15 and we want to solve for t . This inequality involves a linear expression in t .
Distributing First, distribute the 3 on the left side of the inequality:
3 ( 4 − 2 t ) g e 15
12 − 6 t g e 15
Isolating the t term Next, subtract 12 from both sides of the inequality to isolate the term with t :
12 − 6 t − 12 g e 15 − 12
− 6 t g e 3
Dividing by a Negative Number Now, divide both sides of the inequality by -6. Remember that when we divide by a negative number, we must reverse the inequality sign:
− 6 − 6 t l e − 6 3
tl e − 2 1
Final Answer Thus, the solution to the inequality is tl e − 2 1 .
Examples
Imagine you're managing a budget for a school event. You have a certain amount of money to spend, and you need to ensure that your expenses don't exceed that amount. This inequality helps you determine the maximum value of a variable (like the number of items you can buy) while staying within your budget. Understanding and solving inequalities is crucial for making informed financial decisions and staying within constraints in various real-life scenarios.
