College Math Placement Practice Test

What is the solution for t in the inequality 0.1 − 2t ≥ 0.7?

1. t ≥ −0.4

2. t ≤ −0.4

3. t ≤ −0.3

4. t ≥ −0.3

The correct answer is: t ≤ −0.3

To solve the inequality \(0.1 - 2t \geq 0.7\), we start by isolating the term with \(t\). First, we can subtract \(0.1\) from both sides: \[ -2t \geq 0.7 - 0.1 \] This simplifies to: \[ -2t \geq 0.6 \] Next, we divide both sides by \(-2\). Remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign: \[ t \leq \frac{0.6}{-2} \] Calculating that gives: \[ t \leq -0.3 \] Thus, the solution indicates that \(t\) must be less than or equal to \(-0.3\), confirming that the correct choice is one that states \(t\) is less than or equal to \(-0.3\). The reasoning leading to this conclusion reflects an accurate handling of inequalities, particularly the importance of reversing the inequality when dividing by a negative number.