# How do you solve 6r+7=13+7r?

Jul 30, 2016

Isolate $r$ on one side of the equation.

#### Explanation:

In order to do this, let's subtract 7 from each side:

$6 r = 6 + 7 r$

Next, let's subtract $7 r$ from each side:

$- r = 6$

Finally, let's divide each side by -1 to get our answer:

$r = - 6$

Jul 30, 2016

$r = - 6$

#### Explanation:

$\textcolor{b l u e}{\text{Method}}$

Collect the constants on one side of the = and the variables (terms with r ) on the other side. Then manipulate so that you only have a single r on its own on one side and everything else on the other.

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$\textcolor{b l u e}{\text{Applying the method}}$

$\textcolor{b r o w n}{\text{Not using short cuts so that you can see where the shortcuts come}}$$\textcolor{b r o w n}{\text{from.}}$

Subtract $\textcolor{b l u e}{6 r}$ from both sides

$\textcolor{b r o w n}{6 r \textcolor{b l u e}{- 6 r} + 7 \text{ "=" } 13 + 7 r \textcolor{b l u e}{- 6 r}}$

$\text{ "0+7" "=" } 13 + r$

Subtract $\textcolor{b l u e}{13}$ from both sides

color(brown)(7color(blue)(-13)" "=" "13color(blue)(-13)+r

$\text{ "-6" "=" } 0 + r$

$r = - 6$

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The short cut approach for add or subtract is: Move something to the other side of the = and change its sign.