Question

Question #24e48

Answer 1

Your equation has an infinite number of solutions.

Explanation:

Your starting expression looks like this

`6 * (2x + 4) = 10x + 24 + 2x`

Notice that your equation contains two types of terms

• terms that contain `x`
• terms that do not contain `x`

Your goal here is to get all the tems that contain `x` on one side of the equation, and all the terms that do not contain `x` on the othe side of the equation.

So, start by expanding the paranthesis by multiplying both terms by `6`

`6 * (2x + 4) = 6 * 2x + 6 * 4 = 12x + 24`

The equation now looks like this

`12x + 24 = 10x + 24 + 2x`

Notice that you can group two terms that contain `x` on the right-hand side of the equation to get

`12x + 24 = underbrace(12x)_(color(blue)(10x + 2x)) + 24`

Notice that we are left with the same expression on both sides of the equation

`12x + 24 = 12x + 24`

In this case, you would say that the equation has an infinite number of solutions because you can plug in any value of `x` and the equation will be true!

More specifically, this is reduced to

`color(red)(cancel(color(black)(12x))) - color(red)(cancel(color(black)(12x))) = color(red)(cancel(color(black)(24))) - color(red)(cancel(color(black)(24)))`

`0 = 0`

This is true regardless of the value of `x`, which is why the equation is said to have an infinite number of solutions.