Equations with 1 unknown variable

Equations with one unknown variable are fundamental in algebra and serve as a cornerstone for solving various mathematical problems. In the examples provided, each equation is linear and follows the standard form of ax + b = c, where 'a' is the coefficient of the variable, 'x' is the unknown variable to be solved for, 'b' is a constant, and 'c' is the resulting sum. To solve these equations, one must isolate the variable 'x' by performing inverse operations to eliminate 'b' from one side of the equation, allowing 'x' to be determined.

The set of equations given are all structured to be solved by subtracting or adding 'b' from both sides of the equation to isolate the term containing 'x'. This results in a simplified equation of the form ax = d, where 'd' is the adjusted sum after moving 'b'. The final step involves dividing both sides of the equation by 'a' to find the value of 'x'. For instance, in the equation 5a + 2 = 22, subtracting 2 from both sides yields 5a = 20, and then dividing by 5 gives a = 4. This straightforward method of solving is consistently applied across all equations listed, whether the operation involves addition or subtraction of the constant 'b'.