How do you solve #2( 2x + 5) - 7x - 21= 5( - 3+ x ) - 8x + 4#?

Expand and collect like terms:

#2(2x+5) − 7x − 21 = 5(−3+x) − 8x + 4#

#4x + 10 − 7x − 21 = -15 + 5x) − 8x + 4#

#-3x - 11 = -3x - 11#

Since both sides of the equation are the same, that means that there are infinitely many solutions, or all real numbers, or #(-oo, oo)#.

1. Distribute
   #4x+10-7x-21=-15+5x-8x+4#
   PAY ATTENTION TO NEGATIVE SIGNS
2. Combine like terms on both sides of the equation
   #-3x-11=-3x-11#
3. Since we now have both sides of the equation looking exactly the same we know that #x=x# and therefore know that #x# can equal anything.

#2(2x+5) - 7x - 21 = 5(-3 + x) - 8x + 4#

The first thing we want to do is distribute or multiply the value outside of the parenthesis to everything inside it. Let's take a look at #2(2x+5)#:
#2 * 2x = 4x#

#2 * 5 = 10#

When we combine this together we get #4x + 10#

Now let's look at #5(-3 + x)#:
#5 * -3 = -15#

#5 * x = 5x#

When we combine this together we get #5x - 15#

Now let's put these back into the equation:
#4x + 10 - 7x - 21 = 5x - 15 - 8x + 4#

Now we simplify by combining like terms:
#-3x - 11 = -3x - 11#

Add #11# to both sides of the equation:
#-3x = -3x#

Divide both sides by #-3#:
#x = x#

Since we know that #x = x# is true, since a value equals to itself, that means the answer is all real numbers, or #(-oo, oo)#.

Hope this helps!