How do you solve #2.5(x-3)+1.7x=10.8(x+1.5)#?

First step is to expand the terms in parenthesis:

#color(red)(2.5)(x - 3) + 1.7x = color(blue)(10.8)(x + 1.5)#

#(color(red)(2.5) xx x) - (color(red)(2.5) xx 3) + 1.7x = (color(blue)(10.8) xx x) + (color(blue)(10.8) xx 1.5)#

#2.5x - 7.5 + 1.7x = 10.8x + 16.2#

Now group and combine like terms:

#2.5x + 1.7x - 7.5 = 10.8x + 16.2#

#4.2x - 7.5 = 10.8x + 16.2#

Next, we subtract the necessary terms to isolate the #x# terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

#4.2x - 7.5 - color(red)(4.2x) - color(blue)(16.2) = 10.8x + 16.2 - color(red)(4.2x) - color(blue)(16.2)#

#4.2x - color(red)(4.2x) - 7.5 - color(blue)(16.2) = 10.8x - color(red)(4.2x) + 16.2 - color(blue)(16.2)#

#0 - 7.5 - color(blue)(16.2) = 10.8x - color(red)(4.2x) + 0#

#-23.7 = 6.6x#

Now, we can divide each side of the equation by #color(red)(6.6)# to solve for #x# while keeping the equation balanced:

#-23.7/color(red)(6.6) = (6.6x)/color(red)(6.6)#

#-3.59 = (color(red)(cancel(color(black)(6.6)))x)/cancel(color(red)(6.6))#

#-3.59 = x#

#x = -3.59# rounded to the nearest hundredth