I wasn’t very productive — if you believe the numbers game Solving the Equation (3/x) * (3/x) = (x/3): Simple Steps Explained

I wasn’t very productive — if you believe the numbers game! 

Algebraic equations that involve fractions can seem tricky at first glance, but with a step-by-step approach, solving them becomes easy. In this post, we’ll guide you through solving the equation (3/x) * (3/x) =(x/3), breaking it down into simple, manageable steps.

Step 1: Simplify the Left Side

Let’s start by simplifying the left side of the equation. We have:

(3/x) * (3/x)

Multiply the numerators and the denominators:

9/x^2

Now the equation looks like this:

9/x^2 = (x/3)

 

Step 2: Cross Multiply

To eliminate the fractions, cross multiply. This means multiplying both sides of the equation by the denominators. So, we’ll multiply 9 by 3 and x^2 by x:

9 * 3 = x^2 * x

This simplifies to:

27 = x^3

 

Step 3: Solve for x

Now, we need to solve for x. To get rid of the cube, take the cube root of both sides:

x = {27}^(1/3)

The cube root of 27 is 3 because (3 * 3 * 3 = 27).

So, x = 3.

 

Step 4: Check Your Solution

It’s always a good idea to check your solution by substituting it back into the original equation. Let’s substitute x = (3/x) *(3/x) = (x/3)

(3/3) * (3/3) = (3/3)

This simplifies to:

1 * 1 = 1

Since both sides are equal, our solution is correct!

 

Conclusion

By simplifying step by step, we were able to solve the equation (3/x)* (3/x) = (x/3). Cross multiplying and taking cube roots are powerful techniques for solving algebraic fractions. Practice these methods to build your confidence and solve similar equations with ease!

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