Question

I'm studying algebra and I'm having trouble solving the equation −4+x=−2. Can you find the solution to this equation and confirm it using a visual representation, such as a number line?.

Answer 1

To solve the equation \(-4 + x = -2\), we want to isolate \(x\). We can do this by adding 4 to both sides of the equation:

\[
-4 + x + 4 = -2 + 4
\]

This simplifies to:

\[
x = 2
\]

So the solution to the equation is \(x = 2\).

Now, let's confirm this visually using a number line. Below is a representation of a number line:

```
--------------------------------------------------
-4 -3 -2 -1 0 1 2 3 4
^ x
```

1. First, locate \(-4\) on the number line.
2. From \(-4\), we move to the right (since we're adding) to find \(x\).
3. Moving 4 units to the right from \(-4\) brings us to \(0\), and then moving 2 more units to the right from \(0\) brings us to \(2\).

This confirms that when \(x = 2\), substituting back into the original equation:

\[
-4 + 2 = -2
\]

This is true, thus verifying the solution is correct. Hence, the solution to the equation \(-4 + x = -2\) is:

\[
\boxed{2}
\]