MHB Solve for x in the denominator of the fraction

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To solve for x in the equation 7/x = 14, the correct approach involves dividing both sides by 7, resulting in 1/x = 2. Inverting both sides gives x = 1/2. Cross-multiplication is not applicable here since the operation involves addition rather than a fraction comparison. The main solution steps have been clarified, confirming that x equals 1/2 is indeed correct. Understanding the distinction between cross-multiplication and making denominators equal is essential for solving similar problems.
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In this I think you should cross multiply ; I got 1/2 by doing so and I am not sure whether it is correct.Can you help me to solve this and be kind enough to explain your steps a little. :)
 

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Combine terms on the left:

$$\frac{7}{x}=14$$

Divide through by 7:

$$\frac{1}{x}=2$$

Invert both sides:

$$x=\frac{1}{2}$$ :)
 
Many Thanks. :)
 
mathlearn said:
In this I think you should cross multiply ; I got 1/2 by doing so and I am not sure whether it is correct.Can you help me to solve this and be kind enough to explain your steps a little. :)

We cross-multiply when we replace the division symbol with multiplication symbol.

In this case we have addition, where we make denominators equal (and do not cross-multiply).

Main help is already provided by MarkFL.
 
Many Thanks (Smile)
 
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