Answer:
x = 8
Step-by-step explanation:
There are several ways you can solve a proportion like this. Most of the algebraic solutions involve what amounts to multiplying both sides by (4x/3). There are also graphical solutions and solutions that rely on relations that make fractions be equal.
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<h3>cross multiplication</h3>
The method of solution usually recommended is to "clear fractions" and then solve the resulting one-step linear equation. To "clear fractions," multiply both sides of the equation by the least common denominator: 4x.
We describe this as "cross-multiplication" because it looks like each numerator has been multiplied by the opposite denominator.
This "one-step" linear equation is solved by dividing by the coefficient of x, which is 3:
Note that we could have done these operations in one step. The two steps, multiply by 4x and divide by 3, are identical to the one step, multiply by (4x/3).
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<h3>compare fractions</h3>
We can see the solution almost immediately if we rewrite the fractions so they have the same numerator.
The same thing happens if we multiply the equation by the inverse of either side.
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<h3>graphical solution</h3>
If the equation is rewritten to a form that has a value of 0 at the solution, then the x-intercept of the graph will be the solution to the equation.
3/4 = 6/x . . . . . . . . original equation
6/x -3/4 = 0 ⇒ f(x) = 0
f(x) = 6/x -3/4
The graph shows the solution to f(x) = 0 is x=8.