In solving for #x# (the unknown variable), the GOLDEN RULE OF ALGEBRA (COMBINING AND BALANCING THE EQUATION TO SOLVE FOR THE UNKNOWN). (Isolating the variable to get its unknown value)

Steps:

1. Isolate the unknown variable by moving it to the left side of the equation. (also eliminating the other variables to get the final format of #color(blue)(x = ?)#, where #x# is the unknown variable.

2. Combine like terms, balance the equation.

3. Simplify the answer to get the unknown value.

#7x + 6 = 3x + 9#

let's combine the like terms, #7x and 3x# then #6 and 9#

remember the GOLDEN RULE, To balance the equation to get the unknown, to remove the #3x# on the RIGHT side of the equation, we must subtract #-3x# on the RIGHT side, to balance it you must subract #3x# to the LEFT side of the equation.

#color(blue)((-3x))# #7x + 6 = 3x + 9# #color(blue)((-3x)#

#4x + 6 = 9#

we need to isolate the LEFT side of the equation to get the #x = ???# format, to get the unknown value, therefore, we must remove #+ 6#, always remember the GOLDEN RULE, (Balancing the Equation, To get the unknown value)

#color(blue) ((- 6))# #4x + 6 = 9 # #color(blue)((-6))#

#4x = 3 #

to, remove #4# from #4x#, we must divide it both sides of the equation by #4#.

#(cancel(4)x)/cancel(4) = 3/4#

so the final answer is #color(blue)(x = 3/4)#

the other way also like this is also correct,

#7x + 6 = 3x + 9#

#color(blue)((-6))# #7x + 6 = 3x + 9# #color(blue)((-6))#

#7x = 3x + 3#

#color(blue)((-3x))# #7x = 3x# + 3 #color(blue)((-3x))#

#4x = 3#

#cancel((4)x)/4 = 3/4#

#color(blue)(x = 3/4)#

also correct :)