How do you solve #4(x - 5) - 8/-3 = 12#?

1 Answer
Jan 21, 2016

Answer:

#x=22/3#

Explanation:

#color(blue)("~~~~~~~Explaining how to deal with the brackets~~~~~~~~~~~~~~~~~")#
Consider #4(x-5)#

This means there are 4 of #(x-5)#
That is #(x-5)+(x-5)+(x-5)+(x-5)#
From this you observe that it is the same as #4x-20#

The short cut for this is to multiply everything inside the bracket by 4
#color(blue)("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")#

#color(brown)("Given: "4(x-5)-8/(-3)=12)#...........................(1)

#color(purple)("Multiply out the brackets so equation (1) becomes:")#

#color(white)(xxxxxx)4x-20-8/(-3)=12#.................................(2)

#color(purple)("But "-8/(-3)=+8/3" so equation (2) becomes")#

#color(white)(xxxxxx)4x-20+8/3=12#

#color(white)(xxxxxx)4x+(8-60)/3=12#

#color(white)(xxxxxx)4x-52/3=12#..................................(3)

#color(purple)("Add "52/3" to both sides of equation (3) giving:")#

#color(white)(xxxxxx)4x=color(brown)(12+52/3)color(green)( = (36+52)/3)color(blue)(=88/3)#

#color(purple)("Divide both sides by 4 giving:")#

#color(white)(xxxxxx)x=22/3#