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

2 Answers
Jul 30, 2016

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#

Jul 30, 2016

#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.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#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#

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