Question 95372
 five x minus 1 over 9 plus two x plus 4 over 6 equals three x minus four over 3. Solve for x.
:
Assume you mean:
{{{((5x-1))/9}}} + {{{((2x+4))/6}}} = {{{((3x-4))/3}}}
;
Choose a multiplier that is a multiple of all 3 denominators, 18 will work:
18{{{((5x-1))/9}}} + 18{{{((2x+4))/6}}} = 18{{{((3x-4))/3}}}
:
Cancel out the denominators and you have:
2(5x-1) + 3(2x+4) = 6(3x-4)
:
Multiply what's inside the brackets:
10x - 2 + 6x + 12 = 18x - 24
:
16x + 10 = 18x - 24
:
16x - 18x = -24 - 10
:
-2x = -34
:
x = -34/-2
:
x = +17
:
:
Check our solution; substitute 17 for x in the original equation
{{{((5(17)-1))/9}}} + {{{((2(17)+4))/6}}} = {{{((3(17)-4))/3}}}
:
{{{((85-1))/9}}} + {{{((34+4))/6}}} = {{{((51-4))/3}}}
:
{{{((84))/9}}} + {{{((38))/6}}} = {{{((47))/3}}}
:
Put over the common denominator of 18 and you have:
{{{((168))/18}}} + {{{((114))/18}}} = {{{((282))/18}}}; confirms our solution