Certainly! Let's solve the given equation step by step and determine the value that belongs in the box.
We start with the equation:
[tex]\[ 5x - 2 = 4 + 2x \][/tex]
1. First, we need to move all the [tex]\(x\)[/tex] terms to one side of the equation. We do this by subtracting [tex]\(2x\)[/tex] from both sides:
[tex]\[ 5x - 2 - 2x = 4 + 2x - 2x \][/tex]
which simplifies to:
[tex]\[ 3x - 2 = 4 \][/tex]
2. Next, we move the constant term [tex]\(-2\)[/tex] to the other side by adding [tex]\(2\)[/tex] to both sides:
[tex]\[ 3x - 2 + 2 = 4 + 2 \][/tex]
which simplifies to:
[tex]\[ 3x = 6 \][/tex]
3. Finally, we want to isolate [tex]\(x\)[/tex] by dividing both sides of the equation by [tex]\(3\)[/tex]. Therefore, the number that goes in the box is [tex]\(3\)[/tex]:
[tex]\[ \frac{3x}{3} = \frac{6}{3} \][/tex]
[tex]\[ x = 2 \][/tex]
So, the number that we use to divide both sides in the final step is [tex]\(\boxed{3}\)[/tex].
