Answer :
To determine which of the given equations hold true, we need to solve each one individually and see if its solution is valid.
### Option (A) [tex]\(-5m = 25\)[/tex]
Solve for [tex]\(m\)[/tex]:
[tex]\[ -5m = 25 \][/tex]
Divide both sides by [tex]\(-5\)[/tex]:
[tex]\[ m = \frac{25}{-5} = -5 \][/tex]
Check the solution:
[tex]\[ -5(-5) = 25 \quad \text{(True)} \][/tex]
So, option (A) is correct.
### Option (B) [tex]\(-10c = -80\)[/tex]
Solve for [tex]\(c\)[/tex]:
[tex]\[ -10c = -80 \][/tex]
Divide both sides by [tex]\(-10\)[/tex]:
[tex]\[ c = \frac{-80}{-10} = 8 \][/tex]
Check the solution:
[tex]\[ -10(8) = -80 \quad \text{(True)} \][/tex]
So, option (B) is correct.
### Option (C) [tex]\(-7 + g = -12\)[/tex]
Solve for [tex]\(g\)[/tex]:
[tex]\[ -7 + g = -12 \][/tex]
Add [tex]\(7\)[/tex] to both sides:
[tex]\[ g = -12 + 7 = -5 \][/tex]
Check the solution:
[tex]\[ -7 + (-5) = -12 \quad \text{(True)} \][/tex]
So, option (C) is correct.
### Option (D) [tex]\(12m + 20 = -40\)[/tex]
Solve for [tex]\(m\)[/tex]:
[tex]\[ 12m + 20 = -40 \][/tex]
Subtract [tex]\(20\)[/tex] from both sides:
[tex]\[ 12m = -40 - 20 \][/tex]
Simplify the right side:
[tex]\[ 12m = -60 \][/tex]
Divide both sides by [tex]\(12\)[/tex]:
[tex]\[ m = \frac{-60}{12} = -5 \][/tex]
Check the solution:
[tex]\[ 12(-5) + 20 = -60 + 20 = -40 \quad \text{(True)} \][/tex]
So, option (D) is correct.
### Summary of Correct Options
All four options (A), (B), (C), and (D) are correct.
### Option (A) [tex]\(-5m = 25\)[/tex]
Solve for [tex]\(m\)[/tex]:
[tex]\[ -5m = 25 \][/tex]
Divide both sides by [tex]\(-5\)[/tex]:
[tex]\[ m = \frac{25}{-5} = -5 \][/tex]
Check the solution:
[tex]\[ -5(-5) = 25 \quad \text{(True)} \][/tex]
So, option (A) is correct.
### Option (B) [tex]\(-10c = -80\)[/tex]
Solve for [tex]\(c\)[/tex]:
[tex]\[ -10c = -80 \][/tex]
Divide both sides by [tex]\(-10\)[/tex]:
[tex]\[ c = \frac{-80}{-10} = 8 \][/tex]
Check the solution:
[tex]\[ -10(8) = -80 \quad \text{(True)} \][/tex]
So, option (B) is correct.
### Option (C) [tex]\(-7 + g = -12\)[/tex]
Solve for [tex]\(g\)[/tex]:
[tex]\[ -7 + g = -12 \][/tex]
Add [tex]\(7\)[/tex] to both sides:
[tex]\[ g = -12 + 7 = -5 \][/tex]
Check the solution:
[tex]\[ -7 + (-5) = -12 \quad \text{(True)} \][/tex]
So, option (C) is correct.
### Option (D) [tex]\(12m + 20 = -40\)[/tex]
Solve for [tex]\(m\)[/tex]:
[tex]\[ 12m + 20 = -40 \][/tex]
Subtract [tex]\(20\)[/tex] from both sides:
[tex]\[ 12m = -40 - 20 \][/tex]
Simplify the right side:
[tex]\[ 12m = -60 \][/tex]
Divide both sides by [tex]\(12\)[/tex]:
[tex]\[ m = \frac{-60}{12} = -5 \][/tex]
Check the solution:
[tex]\[ 12(-5) + 20 = -60 + 20 = -40 \quad \text{(True)} \][/tex]
So, option (D) is correct.
### Summary of Correct Options
All four options (A), (B), (C), and (D) are correct.
