Question

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

Answer 1

Isolate `r` on one side of the equation.

Explanation:

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

`6r=6+7r`

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

`-r=6`

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

`r=-6`

Answer 2

`r=-6`

Explanation:

`color(blue)("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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`color(blue)("Applying the method")`

`color(brown)("Not using short cuts so that you can see where the shortcuts come")` `color(brown)("from.")`

Subtract `color(blue)(6r)` from both sides

`color(brown)(6rcolor(blue)(-6r)+7" "=" "13+7rcolor(blue)(-6r))`

`" "0+7" "=" "13+r`

Subtract `color(blue)(13)` from both sides

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

`" "-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.