Question 127980
Write an expression for each phrase
:
Let x = "a number"
:
"The reciprocal of 5 less than a number"
{{{1/((x-5))}}}
:
"4 times the reciprocal of twice the number."
4*{{{1/(2x)}}}
:
The word "is" means equal
"The reciprocal of 5 less than a number is 4 times the reciprocal of twice the number."
{{{1/((x-5))}}} = 4*{{{1/(2x)}}}
Same as:
{{{1/((x-5))}}} = {{{4/(2x)}}} 
:
 Find the number.
Cross multiply the above equation:
4(x-5) = 2x
:
4x - 20 = 2x
:
4x - 2x = +20
:
2x = 20
x = {{{20/2}}}
x = 10
:
:
Check solution in original equation:
{{{1/((10-5))}}} = 4*{{{1/(2(10))}}}
{{{1/5}}} = 4*{{{1/(20)}}}
{{{1/5}}} = {{{4/(20)}}}; confirms our solution
:
:
Did this make sense to you? Any questions?