Let's solve the given equations step-by-step.
### Equation 1:
Equation:
[tex]\[ 101m + 300 = 115 \][/tex]
Step-by-step solution:
1. Subtract 300 from both sides to isolate the term with [tex]\( m \)[/tex]:
[tex]\[ 101m + 300 - 300 = 115 - 300 \][/tex]
[tex]\[ 101m = -185 \][/tex]
2. Divide both sides by 101 to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{-185}{101} \][/tex]
The solution for [tex]\( m \)[/tex] is approximately:
[tex]\[ m \approx -1.8316831683168318 \][/tex]
### Equation 2:
Equation:
[tex]\[ 7 - 5m = 15 \][/tex]
Step-by-step solution:
1. Subtract 7 from both sides to isolate the term with [tex]\( m \)[/tex]:
[tex]\[ 7 - 5m - 7 = 15 - 7 \][/tex]
[tex]\[ -5m = 8 \][/tex]
2. Divide both sides by -5 to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{8}{-5} \][/tex]
The solution for [tex]\( m \)[/tex] is:
[tex]\[ m = -1.6 \][/tex]
### Equation 3:
Equation:
[tex]\[ m + 15 = 350 \][/tex]
Step-by-step solution:
1. Subtract 15 from both sides to solve for [tex]\( m \)[/tex]:
[tex]\[ m + 15 - 15 = 350 - 15 \][/tex]
[tex]\[ m = 335 \][/tex]
The solution for [tex]\( m \)[/tex] is:
[tex]\[ m = 335 \][/tex]
### Equation 4:
Equation:
[tex]\[ 14 - 13 = 150 \][/tex]
This equation is incorrect because:
[tex]\[ 14 - 13 = 1 \neq 150 \][/tex]
Hence, this equation does not have a valid solution.
### Summary of Solutions:
1. For the first equation: [tex]\( m \approx -1.8316831683168318 \)[/tex]
2. For the second equation: [tex]\( m = -1.6 \)[/tex]
3. For the third equation: [tex]\( m = 335 \)[/tex]
4. The fourth equation is incorrect and does not provide a valid solution.
Therefore, the values of [tex]\( m \)[/tex] are:
[tex]\[ -1.8316831683168318, -1.6, \text{ and } 335 \][/tex]
