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February 15th, 2016, 06:52 AM  #1 
Newbie Joined: Feb 2016 From: india Posts: 7 Thanks: 0  solve this equation  confused
9x + 3 = 7x + 10 This seems so simple, but I forgot how to do it. Please help! 
February 15th, 2016, 07:16 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra 
The idea is to remove all the $x$s from one side of the equation and everything else from the other. We do it one step at a time, remembering that we must do the same thing to both sides of the equation. $$\begin{aligned} && 9x+ 3 &= 7x+10 \\ &\text{first I will remove the $7x$ from the right by subtracting it} & 9x+37x &= 7x+107x \\ &\text{and group the terms} & \cancelto{2x}{(9x  7x)} + 3 &= \cancelto{0}{(7x  7x)}+10 \\ && 2x + 3 &= 10 \\ &\text{now I will remove the constant $3$ from the left by subtracting it} & 2x+33 &= 10 3 \\ &\text{and group the terms} & 2x+\cancelto{0}{(33)} &= \cancelto{7}{(103)} \\ && 2x &= 7 \\ &\text{and finally, I will remove the coefficient $2$ from the left by dividing it} & {2x \over 2} &= \frac72 \\ &\text{and group the terms} & \cancelto{1}{\frac22}x &= \frac72 \\ && 1x &= \frac72 \\ && x &= \frac72 \end{aligned}$$ 

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