Final answer:
When solving an equation for a variable x, the result should typically be in the form x = (some value), but can also be x on one side with numbers on the other, x = 0, or there may be no solution at all.
Step-by-step explanation:
When solving an equation for a variable x, the ideal result is an equation in the form of x = (some value). This indicates that you have isolated x on one side of the equation and all numerical values or constants on the other. However, the final form might also be x on one side, numbers on the other side if the equation simplifies in such a way, or x = 0 if after solving, you find that x equals zero is the only solution.
Occasionally, you might encounter a situation where there is no solution to the equation, meaning no value of x satisfies the equation. In mathematics, especially when working with linear equations, quadratic equations, or those that can be simplified to one of these forms, we often use substitution and rearrangement to solve for the dependent variable, in this case, x.
An example is the quadratic equation, x² + 1.2 x 10⁻²x - 6.0 × 10⁻³ = 0, which can be solved using the quadratic formula: ax² + bx + c = 0. We aim to reach a solution that gives us a specific value or set of values for x, after applying the necessary algebraic steps.