Question 798458
{{{x}}}= the number
{{{(1/2)x}}}= one half the number (optional step)
{{{(1/2)x+16}}}= one half the number increased by 16 (optional step)
{{{(2/3)x}}}= 2/3 of the number (optional step)
{{{(2/3)x-4}}}= four less than 2/3 of the number (optional step)
 
The problem says (translates into)
{{{(1/2)x+16=(2/3)x-4}}}
 
We could work with fractions, or eliminate denominators.
 
Working with fractions:
{{{(1/2)x+16=(2/3)x-4}}}
{{{16+4=(2/3)x-(1/2)x}}} (Do you need to do this in 2 steps?)
{{{20=(2/3-1/2)x}}}
{{{20=(4/6-3/6)x}}} (optional step)
{{{20=(1/6)x}}}
{{{6*20=6*(1/6)x}}} (optional step)
{{{120=1*x}}}  (optional step)
{{{highlight(x=120)}}}
 
Eliminating denominators:
From {{{(1/2)x+16=(2/3)x-4}}},
we multiply the expressions on both sides of the equal sign times 6 to get
{{{6*((1/2)x+16)=6*((2/3)x-4)}}} (optional step)
{{{6*(1/2)x+6*16=6*(2/3)x-6*4}}} (optional step)
{{{3x+96=4x-24}}}
{{{96+24=4x-3x}}} (Do you need to do this in 2 steps?)
{{{120=(4-3)x}}} (optional step)
{{{120=1*x}}} (optional step)
{{{highlight(x=120)}}}
 
(Number of steps will vary with teacher and student preference).