Solve: ${ \sqrt[3]{6x + 3} - 8 = 5 }$

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Introduction to the Problem

In this article, we will be solving a mathematical equation involving a cube root. The equation is ${ \sqrt[3]{6x + 3} - 8 = 5 }$. This type of equation can be challenging to solve, but with the right steps and techniques, we can find the value of x.

Understanding the Equation

The given equation is ${ \sqrt[3]{6x + 3} - 8 = 5 }$. To solve this equation, we need to isolate the cube root term. We can start by adding 8 to both sides of the equation, which gives us ${ \sqrt[3]{6x + 3} = 13 }$.

Isolating the Cube Root Term

Now that we have isolated the cube root term, we can cube both sides of the equation to eliminate the cube root. This gives us ${ 6x + 3 = 2197 }$.

Solving for x

Next, we need to solve for x. We can start by subtracting 3 from both sides of the equation, which gives us ${ 6x = 2194 }$. Then, we can divide both sides of the equation by 6, which gives us ${ x = \frac{2194}{6} }$.

Simplifying the Expression

To simplify the expression, we can divide 2194 by 6, which gives us ${ x = 364.33 }$.

Conclusion

In this article, we have solved the equation ${ \sqrt[3]{6x + 3} - 8 = 5 }$. We started by isolating the cube root term, then cubed both sides of the equation to eliminate the cube root. Finally, we solved for x and simplified the expression. The value of x is ${ x = 364.33 }$.

Step-by-Step Solution

Here is the step-by-step solution to the equation:

  1. { \sqrt[3]{6x + 3} - 8 = 5 }$

  2. { \sqrt[3]{6x + 3} = 13 }$

  3. { 6x + 3 = 2197 }$

  4. { 6x = 2194 }$

  5. { x = \frac{2194}{6} }$

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