Let's solve the equation step by step to determine the number that belongs in the box:
1. Starting with the equation:
[tex]\[ 5x - 2 = 4 + 2x \][/tex]
2. Subtract [tex]\(2x\)[/tex] from both sides to collect all terms involving [tex]\(x\)[/tex] on one side:
[tex]\[ (5x - 2) - 2x = (4 + 2x) - 2x \][/tex]
Simplifying this, you get:
[tex]\[ 3x - 2 = 4 \][/tex]
3. Add 2 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ (3x - 2) + 2 = 4 + 2 \][/tex]
Simplifying this, you get:
[tex]\[ 3x = 6 \][/tex]
4. Divide both sides by 3 to solve for [tex]\(x\)[/tex]:
[tex]\[ \frac{3x}{3} = \frac{6}{3} \][/tex]
Simplifying this, you get:
[tex]\[ x = 2 \][/tex]
The number that belongs in the box is [tex]\(3\)[/tex].
