To solve the equation \( 5 + 2m = 3 + m \) for \( m \), we will follow a step-by-step approach.
1. Start with the original equation:
[tex]\[ 5 + 2m = 3 + m \][/tex]
2. Isolate the terms involving \( m \) on one side:
To do this, we need to move the term \( m \) on the right-hand side to the left-hand side. We can do this by subtracting \( m \) from both sides of the equation:
[tex]\[ 5 + 2m - m = 3 + m - m \][/tex]
3. Simplify the equation:
On the right-hand side, \( m - m \) cancels out:
[tex]\[ 5 + (2m - m) = 3 + 0 \][/tex]
[tex]\[ 5 + m = 3 \][/tex]
4. Isolate the \( m \) term completely:
To isolate \( m \), we need to remove the constant term 5 on the left-hand side. We can do this by subtracting 5 from both sides of the equation:
[tex]\[ 5 + m - 5 = 3 - 5 \][/tex]
5. Simplify both sides:
This simplifies to:
[tex]\[ m = 3 - 5 \][/tex]
[tex]\[ m = -2 \][/tex]
So, the solution to the equation \( 5 + 2m = 3 + m \) is:
[tex]\[ m = -2 \][/tex]
