Select The Correct Answer From Each Drop-down Menu.Consider This Equation:$(4x)^{\frac{1}{3}} - X = 0$1. The First Step In Solving This Equation Is To $\square$2. The Second Step Is To $\square$3. Solving This Equation

Introduction

In this article, we will guide you through the process of solving a given equation step by step. The equation is $(4x)^{\frac{1}{3}} - x = 0$. We will break down the solution into manageable steps, making it easier to understand and follow along.

Step 1: Isolate the Variable

The first step in solving this equation is to isolate the variable $x$. To do this, we need to get rid of the fraction by multiplying both sides of the equation by the denominator, which is $3$. This will give us:

$$(4x)^{\frac{1}{3}} - x = 0$$

$$3 \times (4x)^{\frac{1}{3}} - 3x = 0$$

$$\boxed{3(4x)^{\frac{1}{3}} - 3x = 0}$$

Step 2: Simplify the Equation

The second step is to simplify the equation by combining like terms. We can start by factoring out the common term $3$ from the first term:

$$3(4x)^{\frac{1}{3}} - 3x = 0$$

$$3(4x)^{\frac{1}{3}} - 3x = 3(4x)^{\frac{1}{3}} - 3x$$

$$\boxed{3(4x)^{\frac{1}{3}} - 3x = 3(4x)^{\frac{1}{3}} - 3x}$$

Step 3: Solve for x

Now that we have simplified the equation, we can solve for $x$. To do this, we need to isolate $x$ on one side of the equation. We can start by adding $3x$ to both sides of the equation:

$$3(4x)^{\frac{1}{3}} - 3x = 0$$

$$3(4x)^{\frac{1}{3}} = 3x$$

$$\boxed{3(4x)^{\frac{1}{3}} = 3x}$$

Next, we can divide both sides of the equation by $3$ to get:

$$(4x)^{\frac{1}{3}} = x$$

Step 4: Cube Both Sides

The next step is to cube both sides of the equation to get rid of the cube root. This will give us:

$$(4x)^{\frac{1}{3}} = x$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$\boxed{(4x)^{\frac{1}{3}} = x}$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

<br/> **Q&A: Solving the Equation $(4x)^{\frac{1}{3}} - x = 0$** ===================================================== **Q: What is the first step in solving the equation $(4x)^{\frac{1}{3}} - x = 0$?** --------------------------------------------------------- A: The first step in solving this equation is to isolate the variable $x$. To do this, we need to get rid of the fraction by multiplying both sides of the equation by the denominator, which is $3$. This will give us: $(4x)^{\frac{1}{3}} - x = 0

$$3 \times (4x)^{\frac{1}{3}} - 3x = 0$$

Q: What is the second step in solving the equation $(4x)^{\frac{1}{3}} - x = 0$?

A: The second step is to simplify the equation by combining like terms. We can start by factoring out the common term $3$ from the first term:

$$3(4x)^{\frac{1}{3}} - 3x = 0$$

$$3(4x)^{\frac{1}{3}} - 3x = 3(4x)^{\frac{1}{3}} - 3x$$

Q: How do we solve for $x$ in the equation $(4x)^{\frac{1}{3}} - x = 0$?

A: To solve for $x$, we need to isolate $x$ on one side of the equation. We can start by adding $3x$ to both sides of the equation:

$$3(4x)^{\frac{1}{3}} - 3x = 0$$

$$3(4x)^{\frac{1}{3}} = 3x$$

Next, we can divide both sides of the equation by $3$ to get:

$$(4x)^{\frac{1}{3}} = x$$

Q: What is the next step in solving the equation $(4x)^{\frac{1}{3}} - x = 0$?

A: The next step is to cube both sides of the equation to get rid of the cube root. This will give us:

$$(4x)^{\frac{1}{3}} = x$$

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

Q: How do we simplify the equation after cubing both sides?

A: After cubing both sides, we can simplify the equation by expanding the left-hand side:

$$\left((4x)^{\frac{1}{3}}\right)^3 = x^3$$

$$(4x)^1 = x^3$$

$$4x = x^3$$

Q: What is the final step in solving the equation $(4x)^{\frac{1}{3}} - x = 0$?

A: The final step is to solve for $x$ by isolating it on one side of the equation. We can start by dividing both sides of the equation by $x$:

$$4x = x^3$$

$$\frac{4x}{x} = \frac{x^3}{x}$$

$$4 = x^2$$

Q: What is the solution to the equation $(4x)^{\frac{1}{3}} - x = 0$?

A: The solution to the equation is $x = \pm 2$.

Conclusion

In this article, we have walked through the steps to solve the equation $(4x)^{\frac{1}{3}} - x = 0$. We have isolated the variable $x$, simplified the equation, and solved for $x$ by cubing both sides and isolating it on one side of the equation. The solution to the equation is $x = \pm 2$.