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

Question

Savannah Anderson · Accepted Answer

#x=-3#

Given: #-2(x-4)=2# #color(magenta)("~~~~~~~~~~ Short Cut Method ~~~~~~~~~~")# Jumping steps by doing some of it in my head!

#-2x-8=2# #2x=6# #x=3#

#color(magenta)("~~~~~~First Principle Method With Extensive explanation~~~~~~~~~~")#

I am choosing to rewrite it like this:

#-1xx2xx(x-2)=2 ...........................Equation (1)# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Consider just the "2xx(x-4)#

This is the same as 2 of #(x-4)#

Which is #color(green)((x-4)+(x-4)->)color(magenta)( x+x-4-4)#

So #2(x-4)-> 2x-8# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Putting this back into #Equation (1)# gives:

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

#color(brown)("Multiplying the bracket by -1 changes the sign of everything inside the bracket")#

#color(brown)(-2x+8=2)# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("'Getting rid' of the 8 on the left hand side")#

Subtract #color(blue)(8)# from both sides.

#color(brown)(-2x+8 color(blue)(-8)=2color(blue)(-8))#

#-2x+0=-6#

Multiply both sides by -1 changing all the signs

#2x=6# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("'Getting rid' of the 2 in "2x)#

Divide both sides by 2. This is the same as #color(blue)(xx1/2)#

#color(brown)(2x color(blue)(xx1/2)=-6color(blue)(xx1/2)) #

#2/2 x = -6/2#

But #2/2 = 1# giving:

#x=-3#

Eva Adamson · Answer

undefined To solve the equation -2(x - 4) = 2, you would first distribute the -2 to both terms inside the parentheses:

-2(x - 4) = 2
-2x + 8 = 2

Then, you would isolate the variable term by subtracting 8 from both sides:

-2x = 2 - 8
-2x = -6

Finally, you would divide both sides by -2 to solve for x:

x = -6 / -2
x = 3