Answer:
3
Step-by-step explanation:
Given:
If fifteen less than two times a number is divided by six more than the number, the result is four less than 9 times the reciprocal of the number.
Question asked:
Find the number ?
Solution:
Let the number be [tex]x[/tex]
As given that:-
15 less than 2 times a number [tex]\div[/tex] 6 more than the number = 4 less than 9 times the reciprocal of the number
Then the equation will be:-
[tex]\frac{2x-15}{6+x} =9\times\frac{1}{x} -4\\\\ \frac{2x-15}{6+x} =\frac{9}{x} -4\\\\ \frac{2x-15}{6+x} =\frac{9-4x}{x} \\ \\[/tex]
By cross multiplication:-
[tex]x(2x-15)=(6+x)(9-4x)\\2x^{2} -15x=6(9-4x)+x(9-4x)\\2x^{2} -15x=54-24x+9x-4x^{2} \\2x^{2} -15x=54-15x-4x^{2} \\[/tex]
By adding both sides by [tex]15x[/tex]
[tex]2x^{2} =54-4x^{2} \\[/tex]
Adding both sides by [tex]4x^{2}[/tex]
[tex]6x^{2} =54[/tex]
Dividing both sides by 6
[tex]x^{2} =9[/tex]
Taking root both sides
[tex]\sqrt[2]{x^{2} } =\sqrt[2]{9} \\x=\sqrt[2]{3\times3} \\x=3[/tex]
Thus, the number is 3.
