To solve for x when it is in the numerator, isolate the fraction on one side, potentially cross-multiply if set equal to another fraction, and then perform any necessary arithmetic or algebraic operations to isolate and solve for x.
To solve for x when x is in the numerator of a fractional equation, you can follow these general steps:
- Isolate the fraction that contains x in the numerator on one side of the equation.
- If the fraction is equal to another fraction, you can cross-multiply and then solve the resultant equation for x.
- If x is part of a more complex expression in the numerator, you may need to use algebraic operations (like subtracting, adding, multiplying, or dividing terms) to isolate x.
- If the equation involves a negative exponent, remember that this denotes a division rather than multiplication, and you may need to flip the construction to the denominator.
- After isolating x, perform any necessary arithmetic operations, such as multiplying the numerators and denominators or simplifying by common factors.
Once x is isolated, you can solve for its value using standard arithmetic operations or algebraic techniques.