How do you solve #2(2+3)+4x=2(2x+2)+6#?

1 Answer
May 28, 2018

Answer:

All real numbers or #(-oo, oo)# in interval notation.

Explanation:

#2(2+3) + 4x = 2(2x+2) + 6#

First, simplify #2(2+3)#:
#color(blue)(2(2+3) = 2(5) = 10)#

Put it back into the equation:
#10 + 4x = 2(2x+2) + 6#

Next, use the distributive property to simplify #2(2x+2)#:
cdn.virtualnerd.com

Following this image, we know that:
#color(blue)(2(2x+2) = (2 * 2x) + (2 * 2) = 4x + 4)#

Put it back into the equation:
#10 + 4x = 4x + 4 + 6#

Add #4+6 = 10#:
#10 + 4x = 4x + 10#

Subtract #color(blue)(4x)# from both sides of the equation:
#10 + 4x quadcolor(blue)(-quad4x)= 4x + 10 quadcolor(blue)(-quad4x)#

#10 = 10#

Oh no! Our variables are gone now. Now we see if this equation is true. It is true that #10 = 10#, meaning that the answer is All real numbers or #(-oo, oo)# in interval notation.

Hope this helps!