Final answer:
To solve the given equations, you need to identify the unknowns and knowns, and then choose an equation to plug in the knowns and solve for the unknown. By following this method, you can find the solutions of the equations.
Step-by-step explanation:
- Identify the unknown.
Unknown: x - Identify the knowns.
Knowns: For equation 1: 18
For equation 2: 37
For equation 3: 12
For equation 4: -20
For equation 5: 54 - Choose an equation, plug in the knowns, and solve for the unknown.
For equation 1: 18 = 3(3x-6)
Simplify the equation: 18 = 9x-18
Add 18 to both sides of the equation: 9x = 36
Divide both sides of the equation by 9: x = 4
Therefore, x = 4 is the solution.
For equation 2: 37 = -3+5(x+6)
Simplify the equation: 37 = -3+5x+30
Combine like terms: 37 = 5x+27
Subtract 27 from both sides of the equation: 10 = 5x
Divide both sides of the equation by 5: x = 2
Therefore, x = 2 is the solution.
For equation 3: 4(-x+4)=12
Simplify the equation: -4x + 16 = 12
Subtract 16 from both sides of the equation: -4x = -4
Divide both sides of the equation by -4: x = 1
Therefore, x = 1 is the solution.
For equation 4: 10(1+3b)= -20
Simplify the equation: 10 + 30b = -20
Subtract 10 from both sides of the equation: 30b = -30
Divide both sides of the equation by 30: b = -1
Therefore, b = -1 is the solution.
For equation 5: -6(1-5v)=54
Simplify the equation: -6 + 30v = 54
Add 6 to both sides of the equation: 30v = 60
Divide both sides of the equation by 30: v = 2
Therefore, v = 2 is the solution.