Final answer:
To solve for x when it's in the denominator, one can cross-multiply if dealing with a proportion, or use algebraic manipulations such as multiplying by the reciprocal of x to move x to the numerator and isolate it.
Step-by-step explanation:
The steps for solving for a variable like x when x is in the denominator will often involve rearranging the equation so that x is no longer in the denominator. If we have a proportion, like a/x = b/c, where we are solving for x, one approach to get x out of the denominator is to cross-multiply. This gives us ac = xb. From here, we would divide both sides by b to isolate x, leading to x = ac/b.
If x is in the denominator of a more complex equation, we may need to perform additional steps, such as multiplying every term by x to clear the denominator, or using the reciprocal of the combined gas law if it applies. When dealing with negative exponents or simplifying fractions in algebra, it's important to remember that negative exponents flip the construction to the denominator, or denote a division rather than multiplication. Therefore, one might sometimes need to multiply by the reciprocal of x.
In summary, to solve for a variable in the denominator, you may cross-multiply in a proportion, multiply by the reciprocal of the variable, or perform any algebraic manipulation necessary to get the variable into the numerator and isolate it on one side of the equation.