What is the Solution to 3x^(-1/2) - 4 = 0?

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Discussion Overview

The discussion revolves around solving the equation 3x^(-1/2) - 4 = 0, focusing on algebraic manipulation and the properties of exponents. The scope includes technical explanations and mathematical reasoning related to algebra.

Discussion Character

  • Technical explanation, Mathematical reasoning, Homework-related

Main Points Raised

  • One participant asks for the solution to the equation 3x^(-1/2) - 4 = 0.
  • Another participant suggests multiplying through by x^(1/2) to simplify the equation, indicating that x must not equal zero.
  • A third participant expresses confusion about the multiplication step and its implications.
  • A later reply attempts to clarify the multiplication process and references the property of exponents to explain the transformation of the first term.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the multiplication step, indicating that there is no consensus on the clarity of the explanation or the next steps in solving the equation.

Contextual Notes

Some participants may be missing foundational assumptions about the properties of exponents and the implications of multiplying by x^(1/2). There is also uncertainty about how to proceed after the multiplication step.

Dil1
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solve the equation
3x^(-1/2) - 4 = 0
 
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I've moved this thread here to our algebra forum since this is a better fit given the question.

We are given to solve:

$$3x^{-\frac{1}{2}}-4=0$$

What do we get if we multiply through by $x^{\frac{1}{2}}\ne0$?
 
MarkFL said:
I've moved this thread here to our algebra forum since this is a better fit given the question.

We are given to solve:

$$3x^{-\frac{1}{2}}-4=0$$

What do we get if we multiply through by $x^{\frac{1}{2}}\ne0$?

i don't get it?
 
Dil said:
i don't get it?

Well if we multiply through by $x^{\frac{1}{2}}$ we have:

$$3x^{-\frac{1}{2}}x^{\frac{1}{2}}-4x^{\frac{1}{2}}=0x^{\frac{1}{2}}$$

Now, for the first term on the left, we can use the following property of exponents:

$$a^{b}\cdot a^{c}=a^{b+c}$$

So, what does this term become?
 

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