   SEARCH HOME Math Central Quandaries & Queries  Question from Simon: I would like to ask if you would be able to explain : linear equation: 2 1/2 (X-1) - x+3 /3 = 4 , the first step shows multiplying by 2 then multiplying by 3. etc. What I don't understand is where the 2 in multiplying by 2 comes from? ( the three is pretty obvious being x+3 /3 (to get rid of the divided by) ) . Thanks for your help. Hi Simon,

If I have this equation to solve

$2 \frac12 (x - 1) - \frac{x+3}{3} = 4$

I would first write the mixed number $2 \frac12$ as an improper fraction, that is $2 \frac12 = \frac52.$ Thus the equation becomes

$\frac52 (x - 1) - \frac{x+3}{3} = 4$

Now I hope you can see why you multiply by $2,$ to eliminate the $2$ in the denominator. Multiplying by $2$ on both sides gives

$5 (x - 1) - 2 \times \frac{x+3}{3} = 2 \times 4$

Now multiply by $3$ to remove the final fraction and then solve the resulting equation.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.