To solve for \( x \) in the equation \( 4x + 1 = 3x - 2 \), we can follow these steps:
1. Move all terms involving \( x \) to one side of the equation and all the constant terms to the other side. This helps in isolating \( x \).
Start by subtracting \( 3x \) from both sides of the equation:
[tex]\[
4x + 1 - 3x = 3x - 2 - 3x
\][/tex]
Simplifying both sides gives us:
[tex]\[
4x - 3x + 1 = -2
\][/tex]
2. Combine the \( x \) terms on the left side of the equation:
[tex]\[
x + 1 = -2
\][/tex]
3. Isolate the variable \( x \) by moving the constant term to the other side. Subtract 1 from both sides:
[tex]\[
x + 1 - 1 = -2 - 1
\][/tex]
Simplifying this gives:
[tex]\[
x = -3
\][/tex]
Thus, the solution to the equation \( 4x + 1 = 3x - 2 \) is:
[tex]\[
x = -3
\][/tex]
