To solve the equation [tex]\( 3x + 2(x - 1) = 2(2x - 3) \)[/tex], let's follow these steps:
1. Distribute on both sides of the equation:
- On the left side, distribute the 2 across [tex]\( (x - 1) \)[/tex]:
[tex]\[
3x + 2(x - 1) = 3x + 2x - 2
\][/tex]
- On the right side, distribute the 2 across [tex]\( (2x - 3) \)[/tex]:
[tex]\[
2(2x - 3) = 4x - 6
\][/tex]
2. Combine like terms:
- On the left side, combine the [tex]\( 3x \)[/tex] and [tex]\( 2x \)[/tex]:
[tex]\[
3x + 2x - 2 = 5x - 2
\][/tex]
- The equation now looks like:
[tex]\[
5x - 2 = 4x - 6
\][/tex]
3. Isolate the variable:
- Move all the [tex]\( x \)[/tex]-terms to one side of the equation by subtracting [tex]\( 4x \)[/tex] from both sides:
[tex]\[
5x - 4x - 2 = -6
\][/tex]
- Simplify:
[tex]\[
x - 2 = -6
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Add 2 to both sides of the equation to isolate [tex]\( x \)[/tex]:
[tex]\[
x - 2 + 2 = -6 + 2
\][/tex]
- Simplify:
[tex]\[
x = -4
\][/tex]
Therefore, the solution to the equation [tex]\( 3x + 2(x - 1) = 2(2x - 3) \)[/tex] is:
[tex]\[
x = -4
\][/tex]
