How do you solve #8x + 40 = 4x#?

Step 1) First, subtract #color(red)(40)# from each side of the equation. This will begin the process of isolate the #x# term while keeping the equation balanced:

#8x + 40 - color(red)(40) = 4x - color(red)(40)#

#8x + 0 = 4x - 40#

#8x = 4x - 40#

Step 2) Subtract #color(red)(4x)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#-color(red)(4x) + 8x = -color(red)(4x) + 4x - 40#

#(-color(red)(4) + 8)x = 0 - 40#

#4x = -40#

Step 3) Divide each side of the equation by #color(red)(4)# to solve for #x# while keeping the equation balanced:

#(4x)/color(red)(4) = -40/color(red)(4)#

#(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = -10#

#x = -10#

When you are solving these types of equations, you want to get the #x#'s on one side of the equation, and everything else on the other. Typically, you want all the #x#'s on the left side, and everything else on the right side.

In this case, we have to "move" the 40 to the right side, and "move" the #4x# to the left side.

To do this, we can first subtract 40 from both sides:
#8x+40=4x#
#8x+40-40=4x-40#

Now we can simplify this equation.
#8x=4x-40#

To get the #4x# onto the left side, we can subtract #4x# from both sides:
#8x=4x-40#
#8x-4x=4x-40-4x#

Simplifying:
#4x=-40#

Now, to get the value of #x#, we can divide both sides by 4:
#\frac{4x}{4}=\frac{-40}{4}#
#x=-10#

So, #x# is equal to #-10#.