How do you solve #3a+13=9a-8#?

1 Answer
Dec 21, 2016

#a = 7/2#

Explanation:

First, isolate the #a# terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

#3a + 13 - color(red)(3a + 8) = 9a - 8 - color(red)(3a + 8)#

#3a - 3a + 13 + 8 = 9a - 3a - 8 + 8#

#0 + 13 + 8 = 9a - 3a - 0#

#13 + 8 = 9a - 3a#

Next, we can combine like terms:

#21 = (9 - 3)a#

#21 = 6a#

Now, solve for #a# while keeping the equation balanced:

#21/color(red)(6) = (6a)/color(red)(6)#

#(3 xx 7)/(3 xx 2) = (color(red)(cancel(color(black)(6)))a)/color(red)(cancel(color(black)(6)))#

#3/3 xx 7/2 = a#

#1 xx 7/2 = a#

#7/2 = a#