Question

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

Answer 1

See a solution process below:

Explanation:

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`

Answer 2

Isolate the variable (`x`) on one side (typically the left) and "move" everything else onto the other (typically the right). Then simplify.

Explanation:

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`.