Alright, let's solve each of the given equations step by step.
### Solving the first equation:
1. The first equation is [tex]\( 3(2x - 3) = -2(3x + 2) \)[/tex].
2. Distribute the constants across the terms inside the parentheses:
[tex]\[ 3 \cdot 2x - 3 \cdot 3 = -2 \cdot 3x - 2 \cdot 2 \][/tex]
[tex]\[ 6x - 9 = -6x - 4 \][/tex]
3. To isolate [tex]\( x \)[/tex], combine like terms by moving terms involving [tex]\( x \)[/tex] to one side and constant terms to the other side:
[tex]\[ 6x + 6x = -4 + 9 \][/tex]
[tex]\[ 12x = 5 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{5}{12} \][/tex]
### Solving the second equation:
1. The second equation is [tex]\( 3x - 5 = 2x + 2 \)[/tex].
2. To simplify, move all terms involving [tex]\( x \)[/tex] to one side and constant terms to the other side:
[tex]\[ 3x - 2x = 2 + 5 \][/tex]
[tex]\[ x = 7 \][/tex]
### Summary:
The two solutions from the equations are:
1. For the first equation, [tex]\( x = \frac{5}{12} \)[/tex].
2. For the second equation, [tex]\( x = 7 \)[/tex].
So the final solutions are [tex]\( x_1 = 0.4166666666666667 \)[/tex] (which is [tex]\( \frac{5}{12} \)[/tex]) and [tex]\( x_2 = 7 \)[/tex].
