How do you solve #2( 2- 2x ) = 4- 8( 1- x ) #?

1 Answer
Jun 5, 2017

Answer:

#x = 2/3 or 0.66dot6#

Explanation:

#2(2 - 2x) = 4 - 8(1 - x)#

We can expand the brackets.

#4 - 4x = 4 - 8(1 - x)#

#4 - 4x = 4 - 8 - - 8x#

#4 - 4x = 4 - 8 + 8x#

#4 - 4x = -4 + 8x#

We can Move the #4# over to the right side.

# - 4x = -4 + 8x - 4#

We can Move the #-8x# over to the left side.

# - 4x - 8x = -4 - 4#

#we can solve these equations.

# -12x = -4 - 4#

# -12x = -8#

We can isolate #x# by moving #-12# to the other side of the equation.

#x = -8 ÷ -12#

#color(blue)(x = 2/3 or 0.66dot6#

We can prove our answer by substituting #2/3# for #x# in the equation and see if we are correct.

#2(2 - 2x) = 4 - 8(1 - x)#

#2(2 - 2 xx 2/3) = 4 - 8(1 - 2/3)#

Now we can use #"BODMAS"# or #"PEMDAS"# to solve the equation.

#"BOMDAS"# = Brackets, Order (Power), Multiplication, Division, Addition and Subtraction

#"PEMDAS"# = Power, Exponents, Multiplication, Division, Addition and Subtraction

#2(2 - 2 xx 2/3) = 4 - 8(1 - 2/3)#

#2(2 - 1 1/3) = 4 - 8(1 - 2/3)#

#2(2 - 1 1/3) = 4 - 8(1/3)#

#2 xx 2/3 = 4 - 8(1/3)#

#2 xx 2/3 = 4 - 2 2/3#

#2 xx 2/3 = 1 1/3#

#1 1/3 = 1 1/3#