Sure, let’s solve each of these equations step-by-step.
### 2. [tex]\( 5t + 28 = 10 \)[/tex]
To solve this equation for [tex]\( t \)[/tex]:
1. Subtract 28 from both sides:
[tex]\[ 5t + 28 - 28 = 10 - 28 \][/tex]
[tex]\[ 5t = -18 \][/tex]
2. Divide both sides by 5:
[tex]\[ t = \frac{-18}{5} \][/tex]
So, [tex]\( t = -\frac{18}{5} \)[/tex].
### 5. [tex]\( 6m + 10 = -2 \)[/tex]
To solve this equation for [tex]\( m \)[/tex]:
1. Subtract 10 from both sides:
[tex]\[ 6m + 10 - 10 = -2 - 10 \][/tex]
[tex]\[ 6m = -12 \][/tex]
2. Divide both sides by 6:
[tex]\[ m = \frac{-12}{6} \][/tex]
So, [tex]\( m = -2 \)[/tex].
### 8. [tex]\( 2(x - 3) = 13 \)[/tex]
To solve this equation for [tex]\( x \)[/tex]:
1. Divide both sides by 2:
[tex]\[ \frac{2(x - 3)}{2} = \frac{13}{2} \][/tex]
[tex]\[ x - 3 = \frac{13}{2} \][/tex]
2. Add 3 to both sides:
[tex]\[ x - 3 + 3 = \frac{13}{2} + 3 \][/tex]
Since [tex]\( 3 = \frac{6}{2} \)[/tex], the equation becomes:
[tex]\[ x = \frac{13}{2} + \frac{6}{2} \][/tex]
[tex]\[ x = \frac{19}{2} \][/tex]
So, [tex]\( x = \frac{19}{2} \)[/tex].
### 11. [tex]\( \frac{2m + 5}{3} = 3m - 10 \)[/tex]
To solve this equation for [tex]\( m \)[/tex]:
1. Multiply both sides by 3 to clear the fraction:
[tex]\[ 3 \cdot \frac{2m + 5}{3} = 3 \cdot (3m - 10) \][/tex]
[tex]\[ 2m + 5 = 9m - 30 \][/tex]
2. Subtract 2m from both sides:
[tex]\[ 2m + 5 - 2m = 9m - 30 - 2m \][/tex]
[tex]\[ 5 = 7m - 30 \][/tex]
3. Add 30 to both sides:
[tex]\[ 5 + 30 = 7m - 30 + 30 \][/tex]
[tex]\[ 35 = 7m \][/tex]
4. Divide both sides by 7:
[tex]\[ m = \frac{35}{7} \][/tex]
So, [tex]\( m = 5 \)[/tex].
In summary, the solutions are:
- [tex]\( t = -\frac{18}{5} \)[/tex]
- [tex]\( m = -2 \)[/tex]
- [tex]\( x = \frac{19}{2} \)[/tex]
- [tex]\( m = 5 \)[/tex]
