Question 378593
Let x = "the number"
: 
Write an equation just as it says:
"one half of a number decreased by two thirds is two less than one fifth
 of the number find the number
{{{1/2}}}x - {{{2/3}}} = {{{1/5}}}x - 2
If we multiply equation by 30, we can get rid of those annoying fractions, results:
15x - 20 = 6x - 30(2) 
15x = 6x - 60 + 20
15x - 6x = -60 + 20
9x = -40
x = {{{(-40)/9}}}
x = -4.44, a rather disappointing number, see if it works in the original equation
:
{{{1/2}}}(-4.44) - {{{2/3}}} = {{{1/5}}}(-4.44) - 2
-2.22 - .67 = -.89 - 2
-2.89 = -2.89; so I guess x = -4.44 is the solutions