#1#. Start by simplifying the left side of the equation.

#5x+15+4x-3=-2x+4+2#

#9x+12=-2x+6#

#2#. Add #2x# to both sides of the equation to get rid of #-2x# on the right side of the equation so that all terms with the variable, #x#, are on the left side of the equation.

#9x# #color(red)(+2x)+12=-2x# #color(red)(+2x)+6#

#11x+12=color(darkorange)0+6#

#11x+12=6#

#3#. Subtract #12# from both sides of the equation to get rid of #12# on the left side of the equation so that all constant terms are on the right side of the equation.

#11x+12# #color(red)(-12)=6# #color(red)(-12)#

#11x+color(darkorange)0=-6#

#11x=-6#

#4#. Divide both sides by 11 to isolate for #x#.

#color(red)((color(black)(11x))/11)=color(red)(color(black)(-6)/11)#

#color(red)((color(blue)cancelcolor(black)(11)color(black)x)/color(blue)cancelcolor(red)(11)color(black)=color(red)(color(black)(-6)/11)#

#color(green)(|bar(ul(color(white)(a/a)x=-6/11color(white)(a/a)|)))#