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February 15th, 2016, 06:52 AM   #1
r3v
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solve this equation - confused

9x + 3 = 7x + 10

This seems so simple, but I forgot how to do it. Please help!
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February 15th, 2016, 07:16 AM   #2
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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.
$$\begin{aligned}
&& 9x+ 3 &= 7x+10 \\
&\text{first I will remove the $7x$ from the right by subtracting it} & 9x+3-7x &= 7x+10-7x \\
&\text{and group the terms} & \cancelto{2x}{(9x - 7x)} + 3 &= \cancelto{0}{(7x - 7x)}+10 \\
&& 2x + 3 &= 10 \\
&\text{now I will remove the constant $3$ from the left by subtracting it} & 2x+3-3 &= 10 -3 \\
&\text{and group the terms} & 2x+\cancelto{0}{(3-3)} &= \cancelto{7}{(10-3)} \\
&& 2x &= 7 \\
&\text{and finally, I will remove the coefficient $2$ from the left by dividing it} & {2x \over 2} &= \frac72 \\
&\text{and group the terms} & \cancelto{1}{\frac22}x &= \frac72 \\
&& 1x &= \frac72 \\
&& x &= \frac72
\end{aligned}$$
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