Mastering College Math: Solving Inequalities with Confidence

Solving inequalities can feel a bit like navigating a labyrinth, can’t it? One moment you think you’re on the right path, and the next, you’re back at the start. But don't worry; by breaking down the steps and understanding the process, you'll find your way to the solution in no time.

So, let’s unravel the mystery behind the inequality 0.1 − 2t ≥ 0.7. It might look intimidating at first glance, but once we isolate the variable, it starts to become more manageable.

Start with the original inequality: [ 0.1 - 2t \geq 0.7 ]

Here’s the thing: to solve for t, we need to get it on one side of the inequality. The first step is to subtract 0.1 from both sides. Easy enough, right? This gives us: [ -2t \geq 0.7 - 0.1 ] Simplifying that left-hand side leads us to: [ -2t \geq 0.6 ]

At this point, take a moment to appreciate what we've done. We are getting closer to isolating t. Now, the next step is where some folks trip up: we need to divide both sides by -2. But hold on a sec! Dividing by a negative reverses the inequality sign. It’s like flipping a pancake; you’ve got to be careful or it all goes sideways!

So we execute the division: [ t \leq \frac{0.6}{-2} ]

Doing the math here leads us to: [ t \leq -0.3 ]

Now, it’s like we’ve crossed a finish line. Easy, right? The solution tells us that t must be less than or equal to -0.3. This means, when faced with options like:

• A. (t \geq -0.4)
• B. (t \leq -0.4)
• C. (t \leq -0.3)
• D. (t \geq -0.3)

The correct answer is neatly tucked away in option C: t ≤ -0.3.

Understanding how to properly handle inequalities is crucial, especially for a College Math Placement Test. It’s a fundamental skill that shows up again and again, whether you’re tackling algebra, calculus, or even real-world problem-solving situations.

Speaking of real-world applications, think about budgeting or planning trips. You often find yourself working with constraints that are defined by inequalities—like spending no more than a certain amount.

In conclusion, with practice, patience, and a solid grasp of the rules—like reversing the inequality sign when dividing by a negative number—you’ll not only impress test graders but also equip yourself with skills that extend beyond the classroom walls. Just remember, tackling math problems can be an adventure! So grab your mathematical toolkit and embrace the journey!