Solve the equation ${ }^{c x} / 2={ }^{a f} / g$ for $x$.
A. $x=2 a f / c g$
B. $x=g a f / 2 c$
C. $x=c a f / 2 g$
D. $x=2 c g / a f$
Answer (1)
To solve the equation 2 c ⋅ x = g a ⋅ f for x , let's work through the steps:
Identify the Equation:
The equation given to us is:
2 c ⋅ x = g a ⋅ f
Clear the Fractions:
To eliminate the fractions, multiply both sides by 2:
c ⋅ x = g 2 a ⋅ f
Isolate x :
Divide both sides by c to solve for x :
x = c ⋅ g 2 a ⋅ f
Select the Correct Option:
Comparing this result with the given options, we see that option A. x = c ⋅ g 2 a ⋅ f matches our result.
Therefore, the correct choice is A . x = c ⋅ g 2 a ⋅ f .
This problem involves understanding how to manipulate algebraic equations, specifically clearing fractions and isolating variables, which is a fundamental skill in high school algebra.
