(77) \( -2 x \geq 2 \)

To solve the inequality \(-2x \geq 2\), start by isolating \(x\). First, divide both sides by -2. Remember, when you divide by a negative number, the inequality sign reverses! This gives you \(x \leq -1\). So, all values of \(x\) less than or equal to \(-1\) satisfy the inequality. Play around with some numbers: test \(x = -2\) (yes, it works!) and \(x = 0\) (nope, not a solution). This type of problem often comes up in real life when dealing with constraints or limits. For example, if a store is offering discounts based on quantity purchased, they might set limits that can be expressed mathematically through inequalities. By understanding how to manipulate these equations, you can better navigate situations that require critical thinking around minimum or maximum values!