Let's solve each equation step by step.
### Solving for [tex]\( n \)[/tex] in the equation [tex]\( 3(2n + 5) = 2n - 9 \)[/tex]:
1. Expand the left side of the equation:
[tex]\[ 3(2n + 5) = 3 \cdot 2n + 3 \cdot 5 = 6n + 15 \][/tex]
So, the equation becomes:
[tex]\[ 6n + 15 = 2n - 9 \][/tex]
2. Move all terms involving [tex]\( n \)[/tex] to one side of the equation by subtracting [tex]\( 2n \)[/tex] from both sides:
[tex]\[ 6n + 15 - 2n = 2n - 9 - 2n \][/tex]
This simplifies to:
[tex]\[ 4n + 15 = -9 \][/tex]
3. Isolate the term with [tex]\( n \)[/tex] by subtracting 15 from both sides:
[tex]\[ 4n + 15 - 15 = -9 - 15 \][/tex]
This further simplifies to:
[tex]\[ 4n = -24 \][/tex]
4. Solve for [tex]\( n \)[/tex] by dividing both sides by 4:
[tex]\[ n = \frac{-24}{4} = -6 \][/tex]
Thus, the value of [tex]\( n \)[/tex] is [tex]\(-6\)[/tex], which corresponds to choice (b).
### Solving for [tex]\( m \)[/tex] in the equation [tex]\( \frac{5m}{3} + 5 = m + 7 \)[/tex]:
1. Eliminate the fraction by multiplying the entire equation by 3:
[tex]\[ 3 \left(\frac{5m}{3} + 5 \right) = 3 (m + 7) \][/tex]
This simplifies to:
[tex]\[ 5m + 15 = 3m + 21 \][/tex]
2. Move all terms involving [tex]\( m \)[/tex] to one side of the equation by subtracting [tex]\( 3m \)[/tex] from both sides:
[tex]\[ 5m + 15 - 3m = 3m + 21 - 3m \][/tex]
This simplifies to:
[tex]\[ 2m + 15 = 21 \][/tex]
3. Isolate the term with [tex]\( m \)[/tex] by subtracting 15 from both sides:
[tex]\[ 2m + 15 - 15 = 21 - 15 \][/tex]
This further simplifies to:
[tex]\[ 2m = 6 \][/tex]
4. Solve for [tex]\( m \)[/tex] by dividing both sides by 2:
[tex]\[ m = \frac{6}{2} = 3 \][/tex]
Therefore, the value of [tex]\( m \)[/tex] is [tex]\( 3 \)[/tex], which corresponds to choice (a).
