How do you solve #-5=-2 (x+1)-2(2- x)#?

1 Answer
Apr 30, 2018

Answer:

No Solution or #cancel(0)#.

Explanation:

#-5 = -2(x+1) - 2(2-x)#

This is how you distribute something:
cdn.virtualnerd.com

Following this image, we know that:
#-2(x+1) = -2 * x - 2 * 1 = -2x - 2#

#-2(2-x) = -2 * 2 - 2 * -x = -4 + 2x#

Now let's put these expressions back into the equation:
#-5 = -2x-2 - 4 + 2x#

Let's color code the like terms on the right side of the equation:
#-5 = color(magenta)(-quad2x) quadcolor(blue)(-quad2quad-quad4) quadcolor(magenta)(+quad2x)#

Combine like terms:
#-5 = -6#

However, now we don't have a variable to solve for! Now we look at whether this equation is true. Is it true that #-5 = -6#? NO!

That means the answer is No Solution or #cancel(0)#.

Hope this helps!