How do you solve and check for extraneous solutions in #2(x + 8) ^ (4/5) - 12 = 150#?
Start by rewriting your equation using the radical form for the term that has the fractional exponent
This can be rewritten as
Raise both sides of the equation to the fifth power
This equation will now produce two solutions
and
Your original equation will thus have two valid solutions and no extraneous solutions.
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To solve and check for extraneous solutions in the equation 2(x + 8)^(4/5) - 12 = 150, follow these steps:
Step 1: Add 12 to both sides of the equation: 2(x + 8)^(4/5) = 162
Step 2: Divide both sides of the equation by 2: (x + 8)^(4/5) = 81
Step 3: Raise both sides of the equation to the power of 5/4: [(x + 8)^(4/5)]^(5/4) = 81^(5/4)
Step 4: Simplify both sides of the equation: x + 8 = 3^5
Step 5: Subtract 8 from both sides of the equation: x = 243 - 8
Step 6: Simplify: x = 235
Step 7: Check the solution by substituting x = 235 back into the original equation: 2(235 + 8)^(4/5) - 12 = 150
The left side of the equation equals 150, which matches the right side. Therefore, the solution x = 235 is valid and not an extraneous solution.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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