True or False:
To solve $-2x = 12$, you would add 2 to both sides of the equation.
The equation provided is \(-2x = 12\). Our goal is to isolate the variable \(x\). In this expression, \(x\) is being multiplied by \(-2\). To isolate \(x\), we must perform the inverse operation of multiplication, which is division. Specifically, we should divide both sides of the equation by the coefficient of \(x\), which is \(-2\). Therefore, the correct approach is \(\frac{-2x}{-2} = \frac{12}{-2}\), resulting in \(x = -6\).
The proposed method suggests adding \(2\) to both sides of the equation. Let's see what happens if we do that: \(-2x + 2 = 12 + 2\), which simplifies to \(-2x + 2 = 14\). This operation does not isolate \(x\) and, in fact, makes the equation more complex rather than solving it. Since the correct method requires division by \(-2\) rather than addition, the statement is incorrect.
Because the proposed method of adding 2 is not the correct way to isolate the variable \(x\) in the given equation, the statement is False.
Imagine you are working on a budget and have an equation representing the total cost of items. If an item costs \$2 each, represented by \(-2x = 12\) (where x might represent a quantity you are trying to find), you would need to divide the total by the price per item to find how many you can afford. Adding or subtracting constants incorrectly would lead to an inaccurate count of your items, demonstrating how crucial it is to apply the correct inverse operations in algebra.