Hailey H.

asked • 09/12/23

finding what x will equal

Find any restrictions on the values of x in the equation. (Enter your answers as a comma-separated list. If there are no restrictions on x, enter NONE.)

1
2

x − 9 = 18

x ≠  


 

 


Doug C.

Hailey, please find a better way to represent your fractions. Does this mean: (1/2) / (x-9) = 18 ? Something else? Use grouping symbols to group more than one term in numerator and/or denominator.
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09/12/23

Hailey P.

Hi Doug, this problem should say 1/2x - 9=18
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09/12/23

1 Expert Answer

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Doug C. answered • 09/12/23

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The equation to solve:

(1/2)x - 9 = 18 (note the grouping symbols around the 1/2. Otherwise could be interpreted as 1/(2x).


Since this equation only contains one fraction, the numerical coefficient of the unknown, it really is not necessary to clear the equation of fractions as a first step.


(1/2)x = 27 (add 9 to both sides)

x = 54 (multiply both sides by 2--the reciprocal of 1/2)


If you did clear the equation of fractions as a 1st step by multiplying every term by 2 the work would look like this:

(1/2)x - 9 =18

x - 18 = 36 (multiply every term by 2)

x = 54 (add 18 to both sides)


The choice of technique is whatever you are comfortable with.

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Doug C.

And if the equation really is 1/(2x) - 9 = 18, there is a restriction on x. x cannot equal 0 (otherwise division by 0). In this case we could multiply every term by 2x, resulting in: 1 - 18x = 36x; 1 = 54x; x = 1/54
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09/12/23

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