How do you solve #4( x + 1) - 5x - 4= 9#?

1 Answer

Answer:

#x = -9#

Explanation:

We are trying to solve for #x# which is an unknown variable. If you plug #x# (after you solve it) back into the equation then one side of the equation should equal the other side. #(9 = 9)#

In algebra we go by the PEMDAS rule. Parenthesis first. You can do this by using the distributive property.

#4(x +1) - 5x - 4 = 9#

Remember distributive property is multiplying what is outside the parenthesis by what is inside. So #4# times #x# is #4x# and #4# times #1# is #4#. You write this out and what is left over that you haven't solved yet.

#4x + 4 - 5x - 4 = 9#

This is what we have so far. Now we can either add up like terms (every number with an #x# attached to it), or add constants (regular plain numbers without #x# attached to it) or if you're really pro you can do both at the same time.

So like terms first:

#4x - 5x# is the same thing as #4 - 5# which is #-1#, so you get

# -1x + 4 - 4 = 9#

Now constants: #4 -4 = 0# so you don't have to write anything it just disappears, it's zero!

Now what we have so far is

#-1x = 9#

And what we do next is divide #-1x# by #-1# and then divide the number on the other side (in this case #9#) also by #-1#. Therefore

#(cancel(-1)x)/cancel(-1) = 9/(-1)#

When we solve this #(9 / (-1))# we get #-9#, so #-9# is the answer.

#x = -9#

Like I said at the beginning, if you plug #-9# back into the equation, if your problem solving was right, then one side should equal the other one. And when we plug #-9# into the parenthesis and solve the left side of the equation, #9 = 9#, so we know for sure our answer is right.

Happy hunting!