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| Math Central | Quandaries & Queries |
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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) ) . |
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
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