Final answer:
The solutions to the equations are x = 19/3 for the first equation and x = 131 for the second equation, after performing algebraic operations to isolate x.
Step-by-step explanation:
To solve the given equations, we need to isolate the variable x on one side of the equation. Let's solve each equation step by step.
Equation 1: 4x - 12 = x + 7
- Start by moving all the x terms to one side by subtracting x from both sides: 4x - x - 12 = 7.
- Simplify the equation to get 3x - 12 = 7.
- Then, move the constant term to the other side by adding 12 to both sides: 3x = 19.
- Finally, divide by the coefficient of x, which is 3, to find the value of x: x = 19/3.
Equation 2: 2x + 133 = 3x + 2
- Begin by moving the x terms to one side by subtracting 2x from both sides: 133 = 3x - 2x + 2.
- Simplify the equation to obtain 133 = x + 2.
- Next, isolate x by subtracting 2 from both sides: x = 133 - 2.
- The solution for x in this equation is x = 131.