(-8-2x)^1/3=(-3-x)^1/3

Jasonbradley

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Jun 16, 2024

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Solving the Equation: (-8-2x)^(1/3) = (-3-x)^(1/3)

This equation involves cube roots, which can be a bit tricky to deal with. However, we can simplify it by using the following properties:

• If a^(1/3) = b^(1/3), then a = b. This means we can get rid of the cube roots by cubing both sides of the equation.

Let's break down the solution step-by-step:

1. Cube both sides:

   [(-8-2x)^(1/3)]^3 = [(-3-x)^(1/3)]^3
   

2. Simplify:

   -8 - 2x = -3 - x
   

3. Solve for x:

   -2x + x = -3 + 8
   -x = 5
   x = -5
   

Therefore, the solution to the equation (-8-2x)^(1/3) = (-3-x)^(1/3) is x = -5.

Important Note: Always check your solutions by plugging them back into the original equation to ensure they are valid. In this case, plugging x = -5 into the original equation does indeed work, confirming that our solution is correct.