Question

for the equation $x + 9 = 0$, to solve for $x$, i should
add 9 to each side
divide 9 by each side
multiply 9 to each side
subtract 5 from each side

Explanation:

Step1: Analyze the equation

We have the equation \( x + 9 = 0 \). To isolate \( x \), we need to get rid of the \( +9 \) on the left side.

Step2: Apply the inverse operation

The inverse operation of addition is subtraction. But looking at the options, the closest correct approach among the given options (even though the options have some inaccuracies in wording, but we analyze based on the options) - Wait, actually, the correct mathematical operation is to subtract 9 from both sides. But among the given options, none of them say subtract 9. Wait, maybe there is a mis - option? Wait, no, let's re - check. Wait, the first option is "add 9 to each side" - if we add 9 to each side, we get \( x + 9+9=x + 18=9\), which is wrong. The second option "divide 9 by each side" - dividing by 9 gives \( \frac{x + 9}{9}=\frac{0}{9}\), \( \frac{x}{9}+1 = 0\), not helpful. Third option "multiply 9 to each side" - \( 9(x + 9)=0\times9\), \( 9x+81 = 0\), not helpful. Fourth option "subtract 5 from each side" - \( x + 9-5=x + 4=- 5\), not helpful. Wait, this must be a mistake in the options. But if we consider the intended operation (maybe a typo in the options, like maybe the first option was supposed to be subtract 9), but based on the given options, there is no correct option. But maybe the question has a typo. Wait, no, maybe I misread. Wait, the equation is \( x + 9 = 0 \), to solve for \( x \), we should subtract 9 from both sides. But among the options, none of them is "subtract 9 from each side". But if we have to choose from the given options, there is an error. However, if we assume that the first option is a mis - wording (maybe "subtract 9" instead of "add 9"), but as per the given options, there is no correct answer. But maybe the question is designed with a mistake.

Wait, maybe I made a mistake. Let's re - check the options again. The first option: "add 9 to each side" - if we add 9 to both sides of \( x + 9 = 0 \), we get \( x+9 + 9=x + 18=9\), which is not solving for \( x \). The second: "divide 9 by each side" - \( \frac{x + 9}{9}=\frac{0}{9}\), \( \frac{x}{9}+1 = 0\), not helpful. Third: "multiply 9 to each side" - \( 9x+81 = 0\), not helpful. Fourth: "subtract 5 from each side" - \( x + 4=-5\), not helpful. So there is a mistake in the options. But if we have to choose the least wrong (or maybe the question intended a different equation), but based on the given equation \( x + 9 = 0 \), none of the options is correct. But maybe the original equation was \( x-9 = 0 \), then adding 9 would be correct. Maybe there is a typo in the equation. If we assume the equation is \( x-9 = 0 \), then adding 9 to each side would be correct. So maybe the equation was mistyped. If we go with the assumption that the equation is \( x - 9=0 \) (a possible typo), then the first option "add 9 to each side" would be correct.

Answer:

Since there is an error in the options provided for the equation \( x + 9 = 0 \) (as the correct operation to solve \( x+9 = 0 \) is to subtract 9 from both sides, which is not an option), but if we assume a typo in the equation (e.g., \( x - 9 = 0 \)), then the answer would be the first option: A. add 9 to each side.